Australian and New Zealand Industrial and Applied Mathematics
The 51st ANZIAM Conference
Outrigger Surfers Paradise, 22 View Avenue
Surfers Paradise QLD
1–5 February 2015
The abstracts of the talks in this volume were set individually by the authors. Only minor typographical changes have been made by the editors. The opinions, findings, conclusions and recommendations
in this book are those of the individual authors.
We are grateful to the organisers of the ANZIAM 2012 conference for providing the template files that
they used for their book.
Editors: Scott W. McCue and Matthew J. Simpson
Email: [email protected]
ISBN: 978-0-9942562-0-1 (softcover)
ISBN: 978-0-9942562-1-8 (portable document format)
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QCIF operates QRIScloud, a Queensland-based large-scale cloud computing and data storage service. Part of a federally-funded, national network of research computing infrastructure, QRIScloud is
designed to provide researchers with access to high-speed, high-capacity computing services.
Using QRIScloud, researchers can:
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• Leverage data collections stored in state and
national nodes
• Integrate access to Queensland-based HPC facilities and specialised cloud services
• Access virtual labs with national communities
• Launch on-demand computation
• Host web services
• Access and use a wide range of existing eResearch services, tools and applications
QRIScloud is managed by QCIF and jointly operated through The University of Queensland and
James Cook University.
Conference Details and History
Organising Committee
• Matthew Simpson (Queensland University of Technology) – Co-Director
• Scott McCue (Queensland University of Technology) – Co-Director
• Peter van Heijster (Queensland University of Technology) – SIAM representative
• Owen Jepps (Griffith University)
• Peter Johnston (Griffith University)
• Barbara Johnston (Griffith University)
• Zoltan Neufeld (University of Queensland)
• Graeme Pettet (University of Queensland)
• Tony Roberts (University of Queensland)
Plenary Speakers Committee
• Stan Miklavcic (University of South Australia) – Chair
• Matthew Simpson (Queensland University of Technology)
• Scott McCue (Queensland University of Technology)
• Kate Miles-Smith (Monash University)
• Georg Gottwald (University of Sydney)
• Michael Plank (University of Canterbury)
• Nigel Bean (University of Adelaide)
• Yvonne Stokes (University of Adelaide)
• Antoinette Tordesillas (University of Melbourne)
Plenary Speakers
• Hugh Possingham (University of Queensland)
• Thomas Witelski (Duke University)
• Leah Edelstein-Keshet (University of British Columbia)
• Anne Juel (University of Manchester)
• Mary Myerscough (University of Sydney)
• Michael Small (University of Western Australia)
• Gary Froyland (University of New South Wales)
• Kerry Landman (University of Melbourne) – 2014 ANZIAM Medallist
• Ngamta Thamwattana (University of Wollongong) – 2014 J.H. Michell Medallist
Past Conference Locations
1966 Kangaroo Island
1967 Adelaide
1968 Hall’s Gap
1969 Victor Harbor
1970 Lorne
1971 Smiggin’s Hole
1972 Wollongong
1973 Surfers Paradise
1974 Lorne
1975 Tanunda
1976 Jindabyne
1977 Terrigal
1978 Broadbeach
1979 Leura
1980 Cowes
1981 Victor Harbor
1982 Bundanoon
1966 Coorong (December)
1999 Mollymook
1983 Perth
2000 Waitangi
1984 Merimbula
2001 Barossa Valley
1985 Launceston
2002 Canberra
1986 Wirrina
2003 Sydney
1987 Wairakei
2004 Hobart
1988 Leura
2005 Napier
1989 Ballarat
2006 Mansfield
1990 Coolangatta
2007 Fremantle
1991 Hanmer Springs
2008 Katoomba
1992 Bateman’s Bay
2009 Caloundra
1993 Hahndorf
2010 Queenstown
1994 Pokolbin
2011 Glenelg
1995 Busselton
2012 Warrnambool
1996 Masterton
2013 Newcastle
1997 Lorne
2014 Rotorua
1998 Coolangatta
The T.M. Cherry Student Prize
A student prize was introduced in 1969 at Victor Harbor and is awarded annually for the best student
talk presented at the conference. In May 1976, ANZIAM (then the Division of Applied Mathematics)
adopted the title “T.M. Cherry Student Prize” in honour of one of Australia’s leading scientists,
Professor Sir Thomas MacFarland Cherry. Past recipients are listed below.
R. Jones
J. Rickard
J. Jones
R. P. Oertel
R. E. Robinson
J. P. Abbott
J. Finnigan
S. Bhaskaran
B. Hughes
P. Robinson
J. R. Coleby
B. Hughes
M. Lukas
A. Plank
G. Fulford
J. Gear
P. Kovesi
A. Kucera
S. Wright
G. Fulford
F. Murrell
A. Becker
K. Thalassoudis
M. Rumsewicz
W. Henry
M. Myerscough
J. Roberts
University of Adelaide
University College London
Mount Stromlo
University of Adelaide
University of Sydney
Australian National University
University of Adelaide
Australian National University
University of Queensland
University of Adelaide
Australian National University
Australian National University
University of New South Wales
University of Wollongong
University of Melbourne
University of Western Australia
University of Wollongong
University of Queensland
University of Wollongong
University of Melbourne
Monash University
University of Adelaide
University of Adelaide
Australian National University
University of Oxford
University of Melbourne
J. Best
S. K. Lucas
A. Tordesillas
S. F. Brown
D. Standingford
B. Barnes
A. Buryak
A. Gore
D. Scullen
S. Cummins
J. Clark
T. Gourlay
E. Ostrovskaya
C. Reid
M. Haese
V. Gubernov
W. Megill
K. Mustapha
J. Looker
C. Fricke
S. Harper
E. Button
M. Haythorpe
S. Cohen
L. Mitchell
S. Butler
J. Caffrey
J. Nassios
D. Khoury
T. Vo
M. Chan
D. Khoury
University of Wollongong
University of Sydney
University of Wollongong
University of Sydney
University of Adelaide
Monash University
Australian National University
University of Newcastle
University of Adelaide
Monash University
University of Sydney
University of Adelaide
Australian National University
Massey University
University of Adelaide
Australian Defence Force Academy
University of British Columbia/University of Wollongong
University of New South Wales
University of Melbourne
University of Melbourne
Massey University
University of Melbourne
University of South Australia
University of Adelaide
University of Sydney
University of Sydney
University of Melbourne
University of Melbourne
University of New South Wales
University of Sydney
University of Sydney
University of New South Wales
The Cherry Ripe Prize
Since 1995 the students have run an alternative competition for the best non-student talk. The past
recipients are listed below.
Natashia Boland
Andrew Pullan
Neville de Mestre
David Stump
Mark McGuinness
Joseph Monaghan
Andy Philpott
Phil Broadbridge
Ernie Tuck
Larry Forbes
Stephen Lucas
Kerry Landman
Vicky Mak
James Sneyd
Geoffry Mercer
Neville de Mestre
Philip Maini
Larry Forbes
Larry Forbes
Darren Crowdy
Martin Wechselberger
Scott McCue
Sheehan Olver
Peter Kim
University of Melbourne
University of Auckland
Bond University
University of Queensland
Victoria University of Wellington
Monash University
University of Auckland
University of Wollongong
University of Adelaide
University of Tasmania
University of South Australia
University of Melbourne
Deakin University
University of Auckland
University of New South Wales
Bond University
University of Oxford
University of Tasmania
University of Tasmania
Imperial College, London
University of Sydney
Queensland University of Technology
University of Sydney
University of Sydney
The J.H. Michell Medal
The J.H. Michell Medal is awarded to outstanding new researchers who have carried out distinguished
research in applied or industrial mathematics, where a significant proportion of the research work has
been carried out in Australia or New Zealand. The past recipients are listed below.
Harvinder Sidhu
Antoinette Tordesillas
Nigel Bean
Stephen Lucas
Mark Nelson
Sanjeeva Balasuriya
Yvonne Stokes
Carlo Laing
Scott McCue
Frances Kuo
Matthew Simpson
Terence O’Kane
Ngamta Thamwattana
University of New South Wales
University of Melbourne
University of Adelaide
University of South Australia
University of Wollongong
University of Sydney
University of Adelaide
Massey University
Queensland University of Technology
University of New South Wales
Queensland University of Technology
CSIRO, Marine and Atmospheric Research
University of Wollongong
The E.O. Tuck Medal
In honour of the late Ernest Oliver Tuck, FAustMS, FTSE and FAA, ANZIAM has instituted a midcareer award for outstanding research and distinguished service to the field of Applied Mathematics.
The inaugural EO Tuck Medals were presented at ANZIAM 2013.
Shaun Hendy
Geoffry Mercer
Victoria University of Wellington and Callaghan Innovation
Australian National University
The ANZIAM Medal
The ANZIAM Medal is awarded on the basis of research achievements or activities enhancing applied
or industrial mathematics and contributions to ANZIAM. The first award was made in 1995. The
past recipients are listed below.
Renfrey Potts
Ian Sloan
Ernie Tuck
Charles Pearce
Roger Grimshaw
Graeme Wake
James Hill
Bob Anderssen
Robert McKibbin
Kerry Landman
University of Adelaide
University of New South Wales
University of Adelaide
University of Adelaide
Loughborough University
Massey University
University of Wollongong
Massey University
University of Melbourne
The AF Pillow Applied Mathematics Top-up Scholarship
The AF Pillow Applied Mathematics Trust offers an annual ‘top-up’ scholarship to a student holding
either an Australian Postgraduate Award (APA) or equivalent award for full-time research in Applied
Mathematics leading to the award of a PhD. The aim of the AF Pillow Applied Mathematics Top-up
Scholarship is to increase the quality of postgraduate students in the field of applied mathematics in
Australia. The past recipients are listed below.
Christopher Lustri
Alex Badran
Michael Dallaston
Hayden Tronnolone
Lisa Mayo
Audrey Markowskei
Queensland University of Technology
University of Wollongong
Queensland University of Technology
University of Adelaide
Queensland University of Technology
Macquarie University
The Organising Committee gratefully acknowledges the financial support of the Mathematical Science
School at Queensland University of Technology (QUT), Hearne Scientific Software, the Queensland
Cyber Infrastructure Foundation (QCIF) and Pearson.
The Organising Committee is especially thankful to CSIRO for sponsoring the following students to
attend the ANZIAM 2015 conference:
David Arnold
Rachelle Binny
Jesse Collis
Saber Dini
Adam Ellery
Ashish Goyal
David Harman
Andrew Holder
Wang Jin
Daniel Ladiges
Michael McCullough
Nicholas Read
Konstantinos Sakellariou
David Skene
Minh Tran
Ada Wing Chi Yan
Andrea Babylon
Chen Chen
Eamon Conway
Carson Drummond
Soorena Ezzati
Adrian Grantham
Xinjiang He
Hamidul Islam
Stuart Johnston
Guiyan Ma
Ellen Muir
Nicolas Rebuli
Kate Saunders
Mingmei Teo
Hayden Tronnolone
Lucas Yiew
Peter Ballard
Luigi Cirocco
Heather Davidson
Tom Dyer
Megan Farquhar
Rachael Griffiths
Alexandra Hogan
Michael Jackson
Laura Karantgis
Karen McCulloch
Ravindra Pethiayagoda
James Reoch
Shrupa Shah
Jakub Tomczyk
James Walker
Ayham Zaitouny
Conference venue
Conference Events, Venues and Facilities
Level 2
The Outrigger floor plan for Level 2 and 4.
Level 4
The conference is being held at Outrigger Surfers Paradise, 22 View Avenue Surfers Paradise QLD.
Conference Reception
A Welcome reception will be held from 6-8pm on Sunday 1 February at the Level 4 Palm Prefunction area. All registered delegates and their accompanying guests are invited.
One Day Workshop
A one-day workshop on Discrete Mathematical Models in the Life Sciences will held in the new Science
and Engineering Centre at Queensland University of Technology, Brisbane, on Friday 6 February
2015. The Plenary Speakers for the one-day workshop are Leah Edelstein-Keshet, Kerry Landman
and Michael Small, who are also the invited speakers for ANZIAM 2015.
Conference Banquet
The banquet dinner will be held at SkyPoint, with pre-dinner drinks from 6:30pm on 4 February
2015 at the venue. SkyPoint is situated on level 77 of the iconic Q1 Building, Surfers Paradise
Boulevard, Surfers Paradise. It is just a short 6 minute walk from central Surfers Paradise and FREE
undercover parking is available for visitors via Hamilton Avenue, disabled parking is available. Public
parking is available nearby at Centro Surfers Paradise in Hanlan St or Bruce Bishop car park on Beach
Refreshment Breaks and Lunches
Morning and afternoon tea and light refreshments will be available in the Pre-Function area outside
Boulevard 2. Lunches are included in the registration fee for delegates and their registered guests.
They will be available after the last presentations of the morning sessions at Deja View Restaurant.
Women in Mathematics Lunch
The Women in Mathematics Special Interest Group is running this special lunch, which will be held at
the Level 4 Palm pre-function area at lunchtime on Tuesday 3 February. The lunch will be hosted by
Dr Joanne Hall and supported by Prof. Nalini Joshi’s Georgina Sweet Australian Laureate Fellowship.
Delegates will receive an email message with a request to RSVP before the conference.
Internet Access
Delegates will be provided internet access from Monday–Thursday. Instructions will be provided at
the registration desk.
Plenary Lectures and Contributed Talks
All invited plenary lectures will take place in Boulevard 1–2. Contributed talks will be held in five
parallel sessions in Boulevard 1, 2, 3 and Palm 1, 2. The duration of each contributed talk will be
fifteen minutes with an additional five minutes for questions and room changes.
Boulevard 2
* denotes student talk.
Boulevard 1
Palm 2
Registration at the ANZIAM desk, Pre-function area
Conference Opening, Boulevard 1–2
Plenary: Prof. Hugh Possingham, University of Queensland
Title: Formulating and solving biodiversity conservation problems
Chair: Scott McCue
Chair: Ed Green
Chair: Rosyln Hickson
Chair: Graeme Hocking
Chair: Shev MacNamara
Graeme Wake Mod- Michael Plank What’s Larry Forbes What is Jerome Droniou A hyelling Growth Variability the catch?
Fluid Turbulence?
brid higher-order numeriin Cell Populations
cal scheme for convectiondiffusion problems
Ali A. Zaidi* Solutions Peter Johnston Aggres- Michael Page Singular- Dylan Lusmore* Using
to an advanced functional sion Model for Wolbachia ities in diffusion-driven a biharmonic equation to
partial differential equa- Flies
extend velocity fields in
tion of the pantographlevel set methods, with
applications to melanoma
tumour growth
Bruce van Brunt A Cell Rebecca Turner* De- Jim Denier The un- Megan
Growth Model Adapted veloping a Model of Bird steady flow due to a spin- GPU accelerated algofor Minimum Cell Size Di- Navigation
ning toroidal mass
rithms for computing
matrix function vector
products student
Morning tea
Boulevard 3
Monday morning
Ellen Muir* A mechanism design approach to
efficient dynamic market
Chair: Frances Kuo
Ian Sloan The ANOVA
decomposition of a nonsmooth function of an infinite number of variables
Carson Drummond*
Making Waves:
Hilbert-Huang Transform
Palm 1
Chair: Josh Ross
John Hearne Mobile
kangaroo to sedentary
Abalone - what scale to
Meksianis Ndii* The
effects of Wolbachia on
dengue transmission dynamics
Chair: Kerry Landman
Rachelle Binny* Defining Moments:
Structure in a Model of
Collective Cell Movement
Catherine Penington
Dying in order:
crowding affects particle
* denotes student talk.
Sergey Suslov Nonlinear
instabilities in a vertical
layer of a ferromagnetic
Habibur Rahman* Effects of oblique
magnetic field on mixed
ferrofluid convection
Chair: Yvonne Stokes
Physics of Suspended
Microchannel Resonators
Boulevard 1
Chair: Tim Moroney
Frank de Hoog Applications of Compressive
Palm 2
Minh Tran* A New
Approach For Solving
A Sparse Linear System
With Periodic Boundary
Stuart Johnston* How Andrea
Josh Chopin* The inmuch information can be Modelling Leptospirosis
fluence of object shape on
obtained from tracking in Livestock and Wildlife
the convergence of active
the position of the leading
contour models for image
edge in a scratch assay?
segmentation student
Plenary: A/Prof. Natalie Thamwattana (2014 J.H. Michell Medallist), University of Wollongong
Title: Mathematical modelling in nanotechnology
Chair: Mary Myerscough
Lunch at Deja View Restaurant
Boulevard 2
Boulevard 3
Monday morning continued
Chair: Jerzy Filar
Jin Liang A Free Boundary Problem for Corporate Bond with Credit
Rating Migration
Xin-Jiang He* A new
closed-form formula for
pricing European options
under a skew Brownian
Guiyuan Ma* Pricing
European options written
on a hard to borrow stock
Palm 1
David Harman* Applying Polynomial Chaos to
Epidemic Models
Pascal Buenzli Curvature effects in the evolution of bone tissues during bone remodelling
Plenary: Prof. Tom Witelski, Duke University
Title: Multiscale dynamics of dewetting fluid films
Chair: Kerry Landman
Chair: Zoltan Neufeld
Chair: Vivien Kirk
Gardiner Ayham
Achilles tendon turnover Tracking and Predicting
and adaptive remodelling Multiple Object Dynamics in a Complex
Environment (Animal’s
Edward Green Mathe- Matthew Chan* Mathmatical models for cell- ematical Modelling of
extracellular matrix inter- Spatial Sorting and Evoactions in tissue develop- lution in a Host-Parasite
Boulevard 2
Boulevard 3
Afternoon tea
Microstructure Interpolation for Macroscopic
Adam Tunney* A new
mode of instability in
compressible boundarylayer flows
Chair: John Knight
Jason Cosgrove* Polar
vortices on celestial bodies
Boulevard 1
* denotes student talk.
Monday afternoon
Tim Moroney Preconditioned finite volume
methods on non-uniform
grids for one-dimensional
fractional diffusion equations
Sankaranarayanan* Fractionalin-space partial differential equations on finite
intervals, boundary conditions, and associated
stochastic processes
Chair: Barbara Johnston
Angstmann From stochastic
processes to numerical
schemes for fractional
DEs, and PDEs
Palm 2
rahela abdul Rahim
The Evaluation of Faculty
Employments Policies Using Markov Chain Model
stochastic analysis approach to placing upper
bounds on solutions to
free boundary problems
Chair: Ian Sloan
Hongmei Zhang The
numerical simulation of
a fractional Black-Scholes
model for European call
Palm 1
Chair: Mick Roberts
John Murray Agentbased modelling of hepatitis B virus infection
and clearance
Chair: Mike Plank
Adam Ellery* Characterising
through a crowded environment with different
obstacle sizes
Saber Dini* Quantifying spatial distributions
using a pair correlation
function based on generalized measures of separation
Ali Eshragh The Complexity of Optimal Experimental Design: A Tour
from Applied Probability
to Experimental Mathematics
James Nichols Modelling reaction-diffusion
systems with anomalous
diffusion using a discrete
time random walk, with
examples in modelling of
* denotes student talk.
Mike Chen Drawing of
microstuctured optical fibres with pressurisation
of the internal channels
Yvonne Stokes The
(un)importance of the
temperature gradient in
fibre drawing
Hayden Tronnolone*
Extruding Complicated
Fluid Structures
Chair: Larry Forbes
Boulevard 1
A monomial transformation for evaluating
two-dimensional nearly
singular boundary element integrals
Hao Wang* Analytical
and numerical solutions
of the multi-term timespace fractionaldiffusion
equations with a fractional Laplacian operator
Shev MacNamara The
wave equation is Toeplitz
plus Hankel
Chair: Peter Johnston
Accurate Approximations
of the Riemann-Stieltjes
Palm 2
Mathematics-in-Industry Special Interest Meeting, Boulevard 1
Mathematics-in-Biology Special Interest Meeting, Boulevard 1
Individual-based model
the spatio-temporal dynamics of Influenza in
Ada Yan* Modelling the
role of innate and adaptive immune responses in
controlling influenza infection
Ashish Goyal* Impact
of delta hepatitis on hepatitis B epidemiology and
optimal intervention policies
Boulevard 2
Boulevard 3
Monday afternoon continued
Relations Between the
Counting Process and
the Markov Modulated
Poisson Process
Jerzy Filar
Flows and Markov Decision Processes
Jeffrey Hunter
comparison of computational techniques of the
key properties of Markov
Chair: Dion O’Neale
Peter Taylor How old
is this bird?
Palm 1
Steve Taylor On solutions of a functional PDE
for cell growth and division
Andrew Black Modelling the evolution of unito multi-cellular life
Matthew Simpson Do
pioneer cells exist?
Alexandra Hogan* Exploring bifurcations and
seasonality in a mathematical model of childhood disease
Mingmei Teo* Optimal vaccine allocation for
structured populations
James McCaw Exploring long-term drivers of
pertussis resurgence and
improved vaccine control
Morning tea
David Arnold* Thinfilm flow in helical channels
Lisa Mayo* The effect
of surface wettability on
droplet dynamics
Sue Ann Chen Osmotically driven deformation
of a stable water film
Boulevard 3
Boulevard 2
Boulevard 1
Plenary: Prof. Leah Edelstein-Keshet, University of British Columbia
Title: Models of cell polarization and motility
Chair: Ed Green
Chair: Bruce Gardiner
Chair: Owen Jepps
Chair: John Sader
* denotes student talk.
Tuesday morning
Bootstrapping methods
for prediction intervals for
solar radiation forecasts
Nonparametric comparison of regression surfaces
to assess the impacts of
vegetation re-growth on
wind fields
Chair: Winston Sweatman
John Boland Spatialtemporal forecasting of
solar radiation
Palm 2
Michelle Dunbar Improving Public Transport
Accessibility via the Optimisation and Synchronisation of Schedules for
Key Transport Modes
Soorena Ezzati* An
Investigation into Probabilistic Constraint in Optimal Power Flow Model
Philipp Braun* A Distributed Optimization Algorithm with an Application to a Smart Grid
Chair: Mark Fackrell
Palm 1
Nicolas Rebuli* Hybrid
Markov chain models for
disease dynamics
James Walker* Inference Methods for First
Few Hundred Studies
Boulevard 2
Chair: Jeffrey Hunter
Michael Jackson* The
Saffman-Taylor instability with a finite amount of
viscous fluid
Scott McCue Selecting
the appropriate SaffmanTaylor finger
Boulevard 1
Chair: Michael Page
Luigi Cirocco* Optimising Revenue for Concentrating Solar Thermal Power Plants with
Limited Thermal Energy
Palm 2
Chair: Silvestru Sever
Wind power simulation
using Correlated Innovation Matrix and Wavelet
Multi-resolution Analysis
Dwi Lestari
Matthew Tam*
Reflection methods for Euclidean distance matrix
Palm 1
Chair: Julia Piantadosi
Women in Mathematics Lunch at the Level 4 Palm pre-function area
Chair: Joanne Hall
Lesley Ward and Nalini Joshi
Free time
ANZIAM AGM, Boulevard 1
ANZIAM Executive Meeting, Boulevard 1
Plenary: Prof. Anne Juel, University of Manchester
Title: Interfacial instabilities on the pore scale
Chair: Larry Forbes
Normal lunch at Deja View Restaurant for delegates
Andrew Holder* The
interaction of acidic tumours and chemotherapy
Wang Jin* Incorporating the effects of
chemotherapeutic drugs
into a multiphase model
of cancer spheroid growth
Boulevard 3
Chair: James Osborne
Tuesday morning continued
(* denotes student talk)
Boulevard 3
Boulevard 2
Boulevard 1
Palm 2
Plenary: A/Prof. Mary Myerscough, University of Sydney
Title: Modelling atherosclerotic plaque formation: Boundaries, balances and bifurcations
Chair: Nalini Joshi
Chair: Harvi Sidhu
Chair: Carlo Laing
Chair: Noel Barton
Chair: Troy Farrell
Jason Sharples Mod- Peter van Heijster A Duncan Farrow Peri- Mark Nelson Biogas
elling the intrinsic dy- geometric approach to odically forced circulation production in anaerobic
namics of bushfire propa- stationary defect solu- near the shore of a lake
gation using plane curva- tions in one space dimenture flow
Claire Miller Spark - a Chen Chen* Macroscale Heather
Davidson* Eamon
new research tool for in- model and boundary con- Geothermal
Spring Mathematical modelling
vestigating novel bushfire ditions for spring mass Temperature Analysis
and numerical simulation
spread concepts
system with fine structure
of nanopores
Nicholas Read* The Lotte Sewalt* A ge- Emma
Greenbank* Tony Miller Efficient
Probability of Bushfire ometric construction of Modelling
Surtseyan and robust iterative soIgnition
shock waves in a tumour Ejecta
lutions of the potential
growth model, incorpoequation applied to modrating the Allee effect
elling of electrochemical
Morning tea
Wednesday morning
Dale Ward DES simulation for modelling patient congestion within a
SA metropolitan hospital
component-bycomponent construction
chooses the weights
Chair: Peter Taylor
Mark Fackrell Modeling the care pathway for
stroke patients
Palm 1
Adrian Noppe* Modeling wound closure in an
epethelial cell sheet using
the Cellular Potts Model
Yan Ding Mathematical
modelling of atherosclerosis - atheoma plaque formation, development and
Md Hamidul Islam*
Continuation of Equilibria of an
Atherosclerosis Model
Lyapunovbased Feedback Design:
State Constraint
Kerry-Lyn Roberts*
Vivien Kirk Dynamics
of systems with three
Chair: Peter van Heijster
Cris Hasan* MixedMode Oscillations and
Canard orbits in Chemical Oscillators
Chair: Mat Simpson
modelling to predict and
prevent osteoarthritis
Boulevard 2
Boulevard 3
David Skene* Modelling Overwash on Ice
Floes by Water Waves
Analysis of novel oscillations of quantized
mechanical energy in
nanooscillator systems
Symmetric 4-body motions
Chair: Vivien Challis
Tom Dyer* Modelling of
graphene oxide and carbon nanotubes in a nematic liquid crystal using
continuum mechanics
Steve Walters* The
flux paradox in gravitational lensing
Palm 2
(* denotes student talk)
Chair: Tim Marchant
Tony Roberts Highorder evolution PDEs
model nonlinear dispersive waves over large
apparent wake angle of a
ship travelling in a fluid
of finite depth
Lucas Yiew* Modelling
the Motions of a Sea Ice
Floe in Waves
Boulevard 1
Wednesday morning continued
Solving DNA Sequencing
Problems by Efficient
Problem Heuristics
Sakellariou* Complex Network Transformations of
Time Series: the Ordinal
Partitions Method
Chair: John Hearne
Lewis Mitchell How
much does your social
network reveal about
you? Predictability and
social information flow
models to understand the
economics of innovation
Palm 1
Boulevard 2
John Mitry* I’ve Got
Fauxs in Different Area
Boulevard 1
Luke Bennetts A transfer matrix method for
multiple wave scattering
in 2d
(* denotes student talk)
Palm 2
Nick Fewster-Young
Existence Results for the
of the atom with Bohr
boundary conditions
Lunch at Deja View Restaurant
Plenary: Prof. Michael Small, University of Western Australia
Title: What is a random graph, and why should we care?
Chair: Mick Roberts
Francis Wood- Chair: John Murray
Chair: Jim Denier
Chair: Luke Bennetts
James Reoch* Multi- Peter Ballard* Calcu- Ying Wan Yap Rarefied Audrey Markowskei*
phase modelling of biolog- lating the probability of gas flow generated by an Scattering of acoustic
ical gel mechanics
an epidemic dying out af- oscillating sphere
plane waves by obstacles
ter the initial outbreak
with corners: the effect
of rounding
Andras Czirok Elasto- Anna
McGann* Daniel
Ladiges* Aimin
plastic tissue deforma- Derivation of Fractional Frequency-domain Monte two-dimensional
tions in multicellular mor- SIR Model
Carlo method for linear volume
oscillatory gas flows
triangular mesh method
Allen-Cahn equations in
irregular domains
James Osborne Multi- Karen
McCulloch* Laura
Karantgis* Shanlin Qin* Numeriscale modelling of mul- Analytical expressions for Steady
Saturated- cal and analytical soluticellular biological sys- infection path probabili- Unsaturated
Water tions of confined subdiffutems: mechanics, devel- ties of an SIR model on Flow in a Sloping Do- sion in three dimensions
opment and disease
small networks
main and its Application
to Landslides
Afternoon tea
Boulevard 3
Catheryn Gray* It’s
not just what you do, it’s
where you do it: Signalling through Akt
Wednesday afternoon
Solutions of the discrete Painlev´e equation
q-P (A∗1 ) which are meromorphic at the origin or
Kate Saunders* The
probability of extreme
rain on your parade given
the El Nio Southern Oscillation
and Criticality
Chair: Chris Lustri
Palm 1
resource maintenance of
sensor networks
Lynne McArthur Depicting the outbreak and
spread of algal blooms
in New South Wales Lagoons using NOVA
Rowena Ball In the beginning, there was hydrogen peroxide: periodicity,
gradients, and chirality at
the dawn of life
Marianito Rodrigo A
nonlinear least squares
approach to time of death
estimation via body cooling
William Holmes Asymmetries in the distribution of gene expression
noise direct spatial organization in the developing
mammalian embryo
Noel Barton How hot is
hot (with reference to a
solar collector)?
Elliot Carr Two-scale
computational modelling
of unsaturated water flow
in soils exhibiting smallscale heterogeneity
Billy Todd Towards an
extended Navier-Stokes
hydrodynamics at the
Tony Roberts
John Knight Lewis Fry
Richardson: pioneer of
finite difference methods
for partial differential
Boulevard 1
Luke Fullard ResidenceTime Distribution of
Heaped and Sloped Powder Layers in a Conical
Mass-Flow Hopper
Nanopterons in a granular chain
Erupting Dusts
Washing sugar pulp with
dirty maths
Chair: Jim Hill
Palm 2
(* denotes student talk)
Pre-dinner drinks and Conference Banquet at SkyPoint, level 77 of Q1 Building
Owen Jepps Influence of
homeostasis on the longtime-limit behaviour of an
autoimmune disease
Mick Roberts Exponential growth and the final
size of an epidemic
Robert Moss Epidemic
detection and forecasting
from surveillance data via
Bayesian estimation
Joshua Ross Computation of epidemic final size
Chair: Jen Flegg
Chair: Steve Taylor
Boulevard 2
Boulevard 3
Wednesday afternoon continued
Jin Hyup Hong On the
Euclidean Dimension of
combustion and logistic
population growth
Nobutaka Nakazono
The Lax pairs of discrete Painlev´e equations
arising from the integer
lattice: (A2 + A1 )(1) case
Yang Shi
and combinatorics of
Coxeter groups and discrete integrable systems
Chair: Nalini Joshi
Palm 1
Boulevard 2
Boulevard 1
Palm 2
Sarthok Sircar Chemotactic adhesion in bacterial flocs in shear flow: a
multi-scale model
Chair: Catherine Penington
Adelle Coster Vesicle
Queues: Insulin Regulation in Glucose Transport
Laing Exact
derivation of a neural field model from a
network of theta neurons
Jennifer Flegg Spatiotemporal mathematical modelling of mutations of the dhps gene
in African Plasmodium
falciparum malaria
Hickson A
model of Ebola for
evaluating control
Chair: James McCaw
Scalar diffraction by a
ensemble of arbitrarily
shaped screens: rigorous
Morning tea
Andrey Pototsky
bility of liquid films
ered by a carpet of
propelled surfactant
Awad Al-Mohy Numerical Algorithms to Compute the Sine and the Cosine of a Matrix
Vivien Challis Can we
optimise the strength of
porous materials?
Sheehan Olver Fast and
stable spectral methods
for PDEs
Chair: Bob Anderssen
Plenary: Prof. Kerry Landman (2014 ANZIAM Medallist), University of Melbourne
Title: Tracing genealogy within Fisher’s travelling wave
Chair: Mat Simpson
Boulevard 3
Thursday morning
Laleh Tafakori Random coefficient autoregressive model and Maximum quasi likelihood estimation
in Infinite Dimensions
and Applications in Uncertainty Quantification
Chair: Lewis Mitchell
Palm 1
Boulevard 2
Chair: Mark Nelson
Edward Waters The vital role of animals in
the transmission of waterborne disease in rural
John Shepherd Modelling Tumour Treatment
using the Single Species
Debadi Chakraborty
Viscoelastic Flows in Simple Liquids Generated by
Vibrating Nanostructures
Boulevard 1
Chair: Frank de Hoog
Bob Anderssen Solving
the Interconversion Equation of Rheology for Sums
of Exponentials
Palm 2
Chair: Mark McGuinness
Melanie Roberts Understanding risk through
virtual sensing: an application to the agricultural
Shinya Miyajima Enclosing solutions of the
delay eigenvalue problem
Lunch at Deja View Restaurant
Plenary: Prof. Gary Froyland, University of New South Wales
Title: Dynamics, Probability, and Predictability
Chair: Peter Taylor
Boulevard 3
Chair: Peter van Heijster
Zoltan Neufeld Mathematical modelling of the
self-renewal of the epidermis
Thursday morning continued
Boris Baeumer Existence, uniqueness and
regularity for a class
of semilinear stochastic
Volterra equations with
multiplicative noise
Palm 1
Chair: Jerome Droniou
Vera Roshchina Condition numbers in conic
feasibility problems
Plenary Sessions
Models of cell polarization and motility
Leah Edelstein-Keshet
University of British Columbia, Canada
[email protected]
In this lecture, I will survey work done over the past few years with group members on modeling the polarization
of motile cells (such as white blood cells), their internal signaling, their temporal dynamics, and their evolving
shapes. I will describe how a combination of biological facts and mathematical models (e.g, reaction diffusion
equations) helped us to gain a better understanding of how internal signaling (of proteins such as Rho GTPases,
PI3K), and the response of the structural proteins (cytoskeleton elements such as actin) can orchestrate some
of the complex and interesting cell motility behaviour. I will describe some recent mathematical analysis
that helped us probe these models, as well as experimental collaborations with Andre Levchenko and William
Contributers to this research include former students and postdoctoral fellows: AFM Maree, AT Dawes, A
Jilkine, Y Mori, WR Holmes, V Grieneisen, and others.
Dynamics, Probability, and Predictability
Gary Froyland
University of New South Wales
[email protected]
Many interesting natural phenomena are hard to predict beyond the immediate future. The medium to longterm behaviours of dynamical systems models of these phenomena are often best studied using probabilistic
approaches. Following a gentle introduction to some fundamental results in ergodic theory, I will illustrate
how functional analytic tools can be used to extract robust structures from chaotic flows in Earth’s oceans and
atmosphere and in Jupiter’s atmosphere.
Interfacial instabilities on the pore scale
Anne Juel
University of Manchester, UK
[email protected]
What links a baby’s first breath to adhesive debonding, enhanced oil recovery, or even drop-on-demand devices?
All these processes involve moving or expanding bubbles displacing fluid in a confined space, bounded by either
rigid or elastic walls. In this talk, we show how spatial confinement may either induce or suppress interfacial
instabilities and pattern formation in such flows.
We demonstrate that a simple change in the bounding geometry can radically alter the behaviour of a fluiddisplacing air finger both in rigid and elastic vessels. A rich array of propagation modes, including symmetric,
asymmetric and localised fingers, is uncovered when air displaces oil from axially uniform tubes that have
local variations in flow resistance within their cross-sections. An unexpected and novel propagation mode
exhibits spatial oscillations formed by periodic sideways motion of the interface at a fixed relative distance
behind the moving finger-tip. The presence of multiple steady and unsteady modes is in contrast to the single,
symmetric mode observed in tubes of regular cross-section, e.g. circular, elliptical, rectangular and polygonal.
Moreover, we show that the experimentally observed states are all captured by a two-dimensional depth-averaged
model for bubble propagation through wide channels with a smooth occlusion, which is similar to a model
describing viscous fingering, but with a spatially varying channel height. Viscous fingering in Hele-Shaw cells
is a classical and widely studied fluid-mechanical instability: when air is injected into the narrow, liquid-filled
gap between parallel rigid plates, the axisymmetrically expanding air-liquid interface tends to be unstable to
non-axisymmetric disturbances. We show how the introduction of wall elasticity (via the replacement of the
upper bounding plate by an elastic membrane) can weaken or even suppress the fingering instability by allowing
changes in cell confinement through the flow-induced deflection of the boundary. The presence of a deformable
boundary also makes the system to additional solid-mechanical instabilities, so that in elastic-walled Hele-Shaw
cells that are bounded by sufficiently thin and elastic sheets, the (fluid-based) viscous fingering instability can
arise concurrently with a (solid-based) wrinkling instability. We study the interaction between these distinct
instabilities, using a theoretical model that couples the depth-averaged lubrication equations for the fluid flow
to the F¨
oppl-von K´
an equations, which describe the deformation of the thin elastic sheet.
Tracing genealogy within Fisher’s travelling wave
Kerry Landman
University of Melbourne
[email protected]
Cell invasion, whereby cells move and undergo cell division into previously unoccupied substrates or tissues,
occurs in tumour growth and wound healing. Continuum models of cell invasion typically employ the wellknown partial differential equation called the Fisher equation (1937). The equation supports travelling wave
solutions, making the population-level behaviour highly predictable. Discrete agent-based models, governed by
agent probabilities, reproduce the population-level behaviour of the Fisher equation. However, individual agent
contributions to the total population, measured by agent lineage, are highly variable. Both behaviours have
been verified in a developmental invasion system. In order to understand such seemingly paradoxical findings,
we examine an intermediate level by tracking of the number of divisions (generation number) that cells undergo
within an invasion wave. The spatial and temporal dynamics of cell generation number is determined two ways,
using agent lineage tracings and a multispecies Fisher equation. An interesting inverse problem arises. Can the
lineage tracings of all agents at any given time be determined through knowledge of the generation distributions?
We answer this question by constructing a generation-dependent Galton-Watson process. The method provides
a potentially useful technique for deducing cell lineage data when imaging every cell is not feasible.
Modelling atherosclerotic plaque formation: Boundaries, balances and bifurcations
Mary Myerscough
University of Sydney
[email protected]
Why do some people develop cardiovascular disease while others with similar risk profiles do not? What causes
plaques to regress? Why does raising HDL (“good cholesterol”) reduce cardiovascular disease in some but not
all cases? Why does atherosclerosis sometimes progress in fits and starts? Can atherosclerotic plaques ever
disappear once they have formed?
At first sight, none of these appears to be a question that can be answered mathematically. But the formation
and progress of atherosclerotic plaques are outcomes of many interlinked biochemical, physiological and cellular
processes. Most of these processes are nonlinear and many are influenced by slow changes in physiological
conditions both in the arteries where the plaques form, and in the body as a whole. I will present models for
the formation of plaques in the artery wall based on ordinary and partial differential equations. The solutions
show a variety of bifurcation behaviour and nonlinear dynamical effects that explain published experimental
outcomes and are relevant to drug therapies that are currently under clinical trial.
Formulating and solving biodiversity conservation problems
Hugh Possingham
The University of Queensland
[email protected]
Conservation science is booming and as it matures many of its components are becoming more quantitative.
Traditionally most conservation scientists have had quantitative training in statistics and sometimes basic
applied mathematics. They rarely, if ever, are trained in operations research. This leaves a huge gap in the field
— particular when one recognizes that conservation is an applied science that is all about achieving conservation
outcomes within a constrained budget.
In this talk I will discuss how we have been formulating and solving nature conservation problems — most of
which have never been formulated before. In particular I will discuss: 1) how to allocate resources across the
globe to minimize species loss 2) how monitoring is first and foremost an optimization problem, not a statistical
problem; and 3) how our software, Marxan, is being used to create marine
and terrestrial reserve systems in over 110 countries.
The tools we have used to formulate and solve these problems are fairly standard— differential equations,
optimal control theory, integer linear programming and simulated annealing. For each example I will define
the problem verbally, then mathematically, with a brief discussion of results. The focus of the examples will
be on problem formulation because I have found that the most significant challenge is formulating the correct
problem and communicating the approach to end users.
These, and other issues, are discussed in an informal way in our centre’s monthly magazine — “Decision Point”
What is a random graph, and why should we care?
Michael Small
University of Western Australia
[email protected]
Complex networks, and in particular scale-free networks (graphs with a power-law degree distribution), have
been observed in a wide range of natural and man-made systems: the Internet and telecommunication networks,
power grids, neuronal networks, social networks and disease transmission networks. However, how to generate
random members of a class of networks (graphs) with a given degree distribution (vertex valency sequence) has
not been properly addressed. While algorithms to generate random networks exist, they all introduce biases in
the specific realisations that result. We introduce an unbiased algorithm to randomly select networks based on
degree distribution (and possibly other properties) and show that typical properties of such graphs differ from
many of the properties claimed of (for example) scale-free networks. This allows us to probe experimentally
obtain network data and seek out atypical features — we can determine, in a statistically quantifiable manner,
exactly what properties of a given network make it special.
Mathematical modelling in nanotechnology
Natalie Thamwattana
University of Wollongong
[email protected]
In this talk, we discuss the mechanical behaviour for non-bonded interactions between various nanostructures by
using applied mathematical modelling techniques and continuum mechanical approach. Particularly, we look at
modelling nanostructures, such as nanotubes, aromatics rings and nanopores, which have potential applications
in nanomedicine and clean energy storage. The talk also touches on modelling polymer chains and proteins
using classical calculus of variations.
Multiscale dynamics of dewetting fluid films
Tom Witelski
National Centre for Epidemiology and Population Health, Australian National University.
[email protected]
Instabilities of thin liquid films spreading on solid surfaces are of great concern for many applications involving
coating flows. Generally called “dewetting instabilities”, several stages of dynamics yield rupture, growth of
dry spots, and ultimately break-up of the film into sets of droplets. These instabilities can be captured by
a lubrication model consisting of a fourth-order nonlinear parabolic PDE for the film height. The long-time
behavior can be reduced to a finite-dimensional system for the dynamics of the remaining droplets as interacting
quasi-steady localized structures. The final stage, “coarsening”, is the successive re-arrangement and merging
of smaller drops into fewer larger drops. Mean field models can be constructed to describe the evolution of the
number of droplets and the distribution of drop sizes yielding macro-scale system properties from the underlying
small-scale nonlinear dynamics.
Normal Sessions
Numerical Algorithms to Compute the Sine and the Cosine of a Matrix
Awad Al-Mohy
King Khalid University, Abha, Saudi Arabia
email: [email protected]
Coauthors: Nicholas Higham and Samuel Relton
The importance of the matrix sine and cosine stems from their role in the solution of second order differential
equations y (t) + Ay(t) = g(t), y(0) = y0 , y 0 (o) = y00 , where A is a square matrix. This equation arises in
finite element semidiscretization of the wave equation. We derive new algorithms to evaluate sin(A) and cos(A)
separately and together employing both Pad´e approximants of the sine function and new rational approximants
to the cosine and sine functions obtained from Pad´e approximants to the exponential function. By rigorous analysis we prove that the algorithms are backward stable in exact arithmetic; and our numerical experiments show
that they behave in a forward stable manner in floating point arithmetic and outperform existing algorithms.
Limited resource maintenance of sensor networks
Maryam Alavi-Shoshtari
University of Auckland, Auckland, New Zealand
email: [email protected]
Coauthors: David E. Williams, Jennifer A. Salmond and Jarip P. Kaipio
Due to the increasing availability of sensors of moderate cost, large scale sensor networks are currently considered
for different tasks. One of these is the monitoring of air quality with several, possibly hundreds of sensors
that may cover an extensive area, or may be difficult to access. Maintenance tasks such as periodic external
calibration of the sensors can be tedious and expensive, or render long periods of data ambiguous. When such
maintenance tasks over the whole network are planned and assessed, the related costs are usually fixed.
In this talk, we consider a maintenance strategy that targets at controlling the calibration schedule, with a
fixed average cost. The strategy is based on modelling the measurement process, focuses on the conditional
stationarity of the model, and takes a decision theoretic approach to detect local disturbances, which may be
due either to the actual change in the environment or malfunction of the sensor. The approach also allows for
controlling the trade-off between the probability of detecting a potential sensor malfunction and the related
degree of errors. As a case study, we consider ozone data from the Metro Vancouver air quality sensor network.
Solving the Interconversion Equation of Rheology for Sums of Exponentials
Bob Anderssen
DPAS CSIRO, Canberra, ACT, Australia
email: [email protected]
Coauthors: Frank de Hoog and Rick Loy
For linear viscoelasticity, the interconversion equation is fundamental. It characterizes, in terms of a linear
Volterra convolution relationship, how, for a linear viscoelastic material, its relaxation modulus G and creep
modulus J are related. Consequently, only a single instrument is required to measure experimentally either G
or J. The interconversion relationship can then be solved to obtain the other. A recent stability analysis has
established that recovering J from G is always stable, whereas that of G from J can be unstable. When G
is modelled as a sum of exponentials, then the interconversion algorithm must be solved for J which will also
be a sum of exponentials. A new algorithm for solving the interconversion equation for this situation will be
From stochastic processes to numerical schemes for fractional DEs, and PDEs
Christopher Angstmann
UNSW, Sydney, Australia
email: [email protected]
Coauthors: Bruce Henry
In this talk I will outline a method of obtaining numerical schemes for certain classes of DEs and PDEs as
well as generalisations to fractional DEs and PDEs. The fundamental idea is to use a discrete time and space
random walk and show that in the diffusive limit, that is the limit as the time and space grid spacings go to zero,
the governing equations of the random walk become the equation of interest. In such a manner the governing
equations of the discrete random walk can then be taken as approximating the diffusion limit equations. As a
the numerical scheme corresponds to the governing equation of a stochastic process the resulting solution must
obey certain regularity conditions. For simple PDEs, such as the diffusion equation, this random walk scheme
corresponds to well known numerical schemes. But in slightly more complicated cases, such as Fokker-Planck
equations, the discrete random walk gives different schemes. In the case of fractional DEs and PDEs a discrete
time random walk is chosen such that the waiting time probability is dependent on the time since rival at the
site. With the appropriate choice of probabilities, fractional derivatives appear in the diffusive limit of the
governing equations.
Examples of where we have used this include solving fractional Fokker-Planck equations, fractional reactiondiffusion equations, as well as a fractional SIR compartment model.
Thin-film flow in helical channels
David Arnold
School of Mathematical Sciences, The University of Adelaide, Adelaide, South Australia, Australia
email: [email protected]
Flows in helical channels have applications to static spiral separators used in mineral processing, and microfluidic
lab-on-a-chip devices used to separate different types of cells in blood test samples. In this talk I will describe
solutions for thin-film flows in helical channels with rectangular cross-section, and arbitrary centreline torsion
and curvature. We characterise the effects of changing the radius and pitch of the channel centreline by
considering the balance of centrifugal and gravitational effects. In a region of the parameter space we see the
emergence of two rotating cells of fluid, a result that may have implications for spiral separators.
Relations Between the Markovian Transition Counting Process and the Markov Modulated Poisson Process
Azam Asanjarani
The University of Queensland, Brisbane, QLD, Australia
email: [email protected]
Coauthors: Sophie Hautphene and Yoni Nazarathy
Comparison of different stochastic processes to find a versatile model for describing observed data in an accurate
manner is a fundamental objective in stochastic modelling. In modelling a variety of phenomena such as queueing
processes, traffic in telecommunication networks, requests for Web pages, the frequency of bank transactions,
rainfall, and optical communications a special Markovian arrival process known as the Markov Modulated
Poisson Process (MMPP) is often applied.
In this talk we revisit the MMPP and introduce an alternative that we call Markovian Transition Counting
Process (MTCP). The latter is simply a point process counting the number of transitions of a finite continuoustime Markov chain. Our motivation for studying the MTCP is due to the fact that this process can serve as
a useful substitute for MMPPs whose arrival rate in any phase is greater than the total rate of leaving that
phase. We focus on mathematical peculiarities of this comparison. Specifically, we show that in the stationary
case, both processes can be set to have the same first and second moments at any time, but different third
moments. In the non-stationary case, we show that these processes have the same first moments but different
second moments.
Modelling Leptospirosis in Livestock and Wildlife
Andrea Babylon
Massey University, Auckland, New Zealand
email: [email protected]
Leptospirosis is a disease resulting from a bacterial infection. It occurs when contaminated material, such as
water polluted with the urine of an infected animal, comes into contact with broken skin, mucus membranes
or is ingested internally. It causes abortions and decreased weight gain in livestock. In humans, symptoms are
usually flu-like and result in an average of six weeks off work. It is the highest occurring occupational disease
in New Zealand with between 80 and 180 cases per year, 60% of which result in hospitalisation.
Two mathematical models are proposed here. The first is a simple model with age structure, of the spreading
of infection in wildlife, originally motivated by the infection in rats in Tanzania. The dynamics of the system,
including fixed points, stability criteria, bifurcation diagrams, the next-generation matrix and basic reproduction
number (R0 ), will be addressed. The second is a cyclical model, showing the dynamics of the infection in farmed
livestock in New Zealand. The system is reset to the initial condition (for livestock) at the beginning of each
year. The limit cycle, bifurcation diagram and quasi-R0 value of the system will be determined.
Both models are used to predict conditions under which the infection will persist in the population, and will be
used to derive protocols for minimising the incidence of disease in humans.
Existence, uniqueness and regularity for a class of semilinear stochastic Volterra equations with
multiplicative noise
Boris Baeumer
University of Otago, Dunedin, New Zealand
email: [email protected]
Coauthors: Matthias Geissert, Mih´
aly Kov´
We consider a class of semilinear Volterra type stochastic evolution equation driven by multiplicative Gaussian
noise. The memory kernel, not necessarily analytic, is such that the deterministic linear equation exhibits a
parabolic character. Under appropriate Lipschitz-type and linear growth assumptions on the nonlinear terms
we show that the unique mild solution is mean-p H older continuous with values in an appropriate Sobolev
space depending on the kernel and the data. In particular, we obtain pathwise space- time (Sobolev-H older)
regularity of the solution together with a maximal type bound on the spatial Sobolev norm. As one of the
main technical tools we establish a smoothing property of the derivative of the deterministic evolution operator
In the beginning, there was hydrogen peroxide: periodicity, gradients, and chirality at the dawn
of life.
Rowena Ball
The Australian National University, Canberra, ACT, Australia
email: [email protected]
Coauthors: John Brindley
The story of the relationship between hydrogen peroxide and life is complex and dynamic, and fraught with
certain natural tensions which have led to human misapprehensions. Modern cells make and break hydrogen
peroxide and, after a long period of misunderstanding when it was reviled as a toxic cell-vandal and saboteur of
gene transcription fidelity, evidence is mounting that its relationship with living organisms is intimate and vital.
Yet non-biologically produced hydrogen peroxide existed in the environment before the first photosynthetic
organisms appeared, and primitive anaerobes must have come to some arrangement with it. From various lines
of evidence we have been led to the hypothesis that the dependence of life on hydrogen peroxide is even far more
ancient,and that this small, energetic, chiral molecule was the agent that enabled the very first non-cellular,
self-replicating and evolving systems of the RNA world. In this presentation I will report some key tests that
support this hypothesis. Numerical simulations show that the thiosulfate-hydrogen peroxide (THP) thermopH oscillator can drive RNA replication and RNA enzyme activity, effectively driving evolution of the RNA
world. In a spatially extended system the pH oscillations manifest as travelling waves, so the THP oscillator
may have initiated the ubiquitous dependence of all life on pH gradients. I will discuss how consideration of
the unique physical properties of hydrogen peroxide can explain outstanding mysteries of the origin of life: 1)
its chirality makes the evolution of homochiral biology inevitable, and 2) its high surface tension provides a
favourable environment for vesicles or proto-cells to form. An interesting and more subtle point is that in each
of its actions on the RNA world - direct and indirect, physical and chemical - hydrogen peroxide is effectively
preparing the RNA world for continued existence, evolution, and reliance on an alternative energy source in its
Calculating the probability of an epidemic dying out after the initial outbreak
Peter Ballard
University of Adelaide, Adelaide, SA, Australia
email: [email protected]
After an initial outbreak, an epidemic may go extinct (“epidemic fade-out”), or become endemic due to sufficient
replenishment of susceptible individuals. We consider the probability of epidemic fade-out in the Markovian
SIRS (susceptible-infectious-recovered-susceptible) model. An exact calculation is computationally intensive,
while previously published approximations are not always accurate. We propose a simplified computation
method. This gives only a small error, and is fast enough to be practical even for large population sizes.
Solving DNA Sequencing Problems by Efficient Traveling Salesman Problem Heuristics
Pouya Baniasadi
Flinders University, SA, Australia
email: [email protected]
The ground-breaking discovery of DNA structure in the 1950s opened up an unparalleled opportunity for multidisciplinary efforts, such as the multibillion dollar Human Genome Project, to come together in a quest for
understanding “life”. Mathematics has proved to be vital in many such efforts, specifically the DNA Sequencing
Problem; aligning and merging fragments of DNA to construct the original sequence.
The importance and mathematical beauty in the DNA-Sequencing Problem stem from its close ties to fundamental problems in Combinatorial Optimization and Complexity Theory. In particular, the basic idealized
DNA-sequencing Problem can be easily embedded in a Traveling Salesman Problem (TSP) which, arguably,
is the most widely studied problem in combinatorial optimization thanks to its theoretical importance and
its wide range of applications. While the close relationship between the two problems is underexploited due
to the computational difficulty of TSP, recent advances in the quality of TSP heuristic algorithms provide a
compelling opportunity for a new approach to DNA-Sequencing Problem. Our project is aimed at exploring
this opportunity for developing TSP-based models and algorithms to advance our mathematical understanding
of the DNA-Sequencing Problem as well as offering practical solutions to the DNA-sequencing Problem.
How hot is hot (with reference to a solar collector)?
Noel Barton
Sunoba Pty Ltd, Macquarie Park, NSW, Australia
email: [email protected]
A heat transfer analysis is presented for a gas-cooled solar collector for domestic space heating, process heat or
power generation. The heat transfer gas flows along a duct enclosed within an insulated box. Solar radiation
enters the collector assembly through a double-glazed window with a low-emissivity coating. The geometry of
the collector is invariant in the flow direction.
The model includes convective heat transfer to the gas flow in the duct, molecular diffusion of heat in the
insulation and in the air-gap of the double-glazed window, molecular diffusion of heat in the outer glass sheet of
the window, and convective heat transfer from the window to the surrounding atmosphere. Effects of infrared
radiation are included, as are absorption of solar and infrared radiation in the outer glass sheet.
The model equations are solved by a combined analytical-numerical approach compact enough to be coded in
a spreadsheet. Checks and examples will be given.
A transfer matrix method for multiple wave scattering in 2d
Luke Bennetts
Uni Adelaide, Adelaide, SA, Australia
email: [email protected]
Coauthors: Fabien Montiel
A new method will be outlined to solve time-harmonic multiple wave scattering problems in 2d. The method
uses a decomposition of the 2d domain into slabs. Transfer matrices, which map wave fields from one side of a
slab to the other, are derived using integral transforms. The method is designed for problems involving large
numbers of scatterers and disordered arrays of scatterers, for which direct methods are not effective.
A stochastic analysis approach to placing upper bounds on solutions to free boundary problems.
Louis Bhim
The University of Sydney, Sydney, NSW, Australia
email: [email protected]
Coauthors: Reiichiro Kawai
We approach the problem of placing tight bounds on solutions to obstacle style free boundary problems by
bounding the stochastic representation for the solution using results from stochastic analysis. After establishing
this bound we then formulate the problem as a semidefinite programming problem and tighten the bounds
using numerical optimization. This approach makes use of the Dynkin formula from stochastic analysis to
obtain the bound and sums of squares relaxations to arrive at a computationally tractable problem. We also
discuss applications of this approach to the problem of pricing American style options and the potential for this
approach to be extended to bound solutions to more general free boundary problems.
Defining Moments: Spatial Structure in a Model of Collective Cell Movement
Rachelle Binny
University of Canterbury, Christchurch, New Zealand
email: [email protected]
The ability of cells to migrate plays a fundamental role in tissue repair, development and the immune response.
Pathologies such as cancer can arise when the regulatory mechanisms controlling this movement are disrupted.
Interactions occurring at the level of individuals may lead to the development of spatial structure which will affect
the dynamics of migrating cells at a population level. Models that try to predict population-level behaviour often
take a mean-field approach, which assumes that cells interact with one another in proportion to their average
density and ignores the presence of small-scale spatial structure. In this talk, we will describe an individualbased model (IBM) that uses random walk theory to model stochastic interactions occurring at the scale of
individual migrating cells in continuous space. The IBM incorporates a mechanism for local directional bias such
that an individual’s direction of movement is dependent on the degree of cell crowding in its neighbourhood.
We will then discuss an alternative to the mean-field approach which employs spatial moment theory in order
to account for spatial structure and predict how individual-level interactions propagate to the scale of the whole
Modelling the evolution of uni- to multi-cellular life
Andrew Black
University of Adelaide, Adelaide, Australia
email: [email protected]
The transition from uni-cellular life to multi-cellular is one of the best known examples of the emergence of a
new level of biological organisation. To understand how this transition proceeded we need to know how early
groups of cells came to have the properties needed for Darwinian evolution, i.e. groups must possess some
form of reproduction with heritable variations in fitness. In this talk I will present some recent work towards
modelling the very early stages of this transition and the emergence of crude forms of group level reproduction
in a system in which groups can form when individual cells remain attached to their parents after reproduction.
Spatial-temporal forecasting of solar radiation
John Boland
University of South Australia, Mawson Lakes, Australia
email: [email protected]
Coauthors: Ted Soubhdan
We apply the Combined Autoregressive Dynamical System (CARDS) solar forecasting tool, developed at the
University of South Australia, to forecasting of solar radiation series at three sites in Guadeloupe in the
Caribbean. After performing the model estimates at each individual site, forecast errors were tested for cross
correlation. It was found that on an hourly time scale, there was small but significant correlation between
sites, and this was taken into account in refining the forecast. Cross correlation was found to be insignificant
at the ten minute time scale so this effect was not included in the forecasting. Also, the final error series in
each case was tested for an Autoregressive Conditional Heteroscedastic (ARCH) effect, finding that to construct
prediction intervals for the forecast a conditional forecasting model had to be constructed for the variance. Note
that cross correlation between sites has to be included for this procedure as well as in the forecasting of the
A Distributed Optimization Algorithm with an Application to a Smart Grid
Philipp Braun
University of Bayreuth, 95440 Bayreuth, Germany
email: [email protected]
Coauthors: Lars Gr¨
une, Christopher Kellett, Steven Weller and Karl Worthmann
We present a novel hierarchical scheme for optimal control of large scale systems. The scheme is based on
distributed controllers connected to a central entity. The distributed optimization ensures flexibility while the
central entity coordinates the exchange of information. The algorithm is compared with a fully centralized and
a fully decentralized optimal control scheme. We prove that the distributed control scheme generates the same
results as the centralized control scheme.
We illustrate the results of the control schemes applied to a model of a residential level electricity network
with distributed power generation and distributed storage devices. The algorithms are used in a model predictive control framework to compute optimal charging/discharging rates of the storage devices to reduce the
fluctuations in the power demand over the entire network based on predicted load and predicted generation.
Exact non-classical symmetry solutions of reaction-diffusion equations: Arrhenius combustion
and logistic population growth.
Phil Broadbridge
La Trobe University, Melbourne, VIC, Australia
email: [email protected]
Only a special class of reaction-diffusion equations has full non-classical reductions to solutions that are not invariant under Lie’sclassical symmetries. However some of those equations have important applications. For 1+1
dimensional linear diffusion with a nonlinear reaction, only equations such as the Fitzhugh-Nagumo equation,
and the Huxley equation, with cubic source terms, have strictly non-classical invariant solutions. Under the
assumptions set down by Fisher in 1930, the advance of a new advantageous gene through a diploid population
is governed not by Fisher’s equation but by Huxley’s equation.
For nonlinear reaction-diffusion equationsin n spatial dimensions, there is a single restriction relating nonlinear
diffusivity to nonlinear reaction that always allows non-classical reduction to the linear Helmholtz equation.
This allows us to construct unsteady solutions to a reaction-diffusion equation with any differentiable reaction
term. We demonstrate the radial solutions with logistic source term of population dynamics, and with Arrhenius reaction term of combustion, that follows from the Gibbs non-analytic temperature-dependent canonical
probability distribution. The extinguishing solution is stable to small perturbations.
Curvature effects in the evolution of bone tissues during bone remodelling
Pascal Buenzli
School of Mathematical Sciences, Monash University, Clayton, VIC, Australia
email: [email protected]
Coauthors: Almie Alias
Bone tissues undergo continual remodelling by cells resorbing old, damaged bone and other cells re-forming new
bone. The evolution of the bone interface during resorption and formation is determined in particular by the
local surface cell density. A significant influence on surface cell density is the contraction or expansion of the
local surface area (depending on curvature) when the surface undergoes resorption or formation.
In this contribution, we propose a continuous mathematical model of bone formation to simulate the co-evolution
of the bone interface and of the surface cell density. The concentration or dilution of surface cell density by
the contracting or expanding bone surface requires a regularisation of the equations, specified in the model as a
diffusive redistribution of the cells. Depending on the strength of cell diffusion, initial undulations of the bone
interface either (i) oscillate such that concave regions become convex and convex regions become concave, or (ii)
become smoothed out at different rates. The model is compared with in-vitro experiments of bone deposition
on substrates of different geometries. Finally, a general mathematical framework based on the level-set method
is developed to describe the systematic effects of substrate geometry on tissues or materials that change shape
through formation or resorption by cells from the surface. The advantage of the level-set based framework is to
avoid parameterisation of the surface, which enables the consideration of topological changes of the surface as
may occur for example in osteoporosis.
Two-scale computational modelling of unsaturated water flow in soils exhibiting small-scale heterogeneity
Elliot Carr
Queensland University of Technology, Brisbane, QLD, Australia
email: [email protected]
Coauthors: Ian Turner and Patrick Perr´e
Unsaturated water flow refers to flow in a partially saturated porous medium where the pores are filled with
air in addition to water. A classical continuum description of the process is given by Richards’ equation, a
simplified two-phase model based on Darcy’s Law, taking the form of a single PDE for the water saturation (or
equivalent). For the case when the domain exhibits small-scale heterogeneities in hydraulic properties, numerical
solution of the problem is prohibitively expensive due to the excessive mesh resolution required to capture the
fine detail. This talk presents a two-scale computational model for overcoming this issue for a specific subset of
such problems. The resulting two-scale numerical simulations are shown to produce good qualitative agreement
with the full fine-scale model with a significant reduction in computation time.
Viscoelastic Flows in Simple Liquids Generated by Vibrating Nanostructures
Debadi Chakraborty
Department of Mathematics and Statistics, The University of Melbourne, Melbourne, Victoria-3010, Australia
email: [email protected]
Coauthors: Matthew Pelton, Edward Malachosky, Philippe Guyot-Sionnest and John E. Sader
Newtonian fluid mechanics, in which the shear stress is proportional to the strain rate, is synonymous with the
flow of simple liquids like water. While this paradigm holds widely, the fluid-structure interaction of mechanical
devices at nanometre scales can probe the intrinsic molecular relaxation processes in a surrounding liquid. In
this talk, I will report our recent theoretical and experimental work on the non-Newtonian, viscoelastic flow
phenomena produced by the high-frequency (¿20 GHz) vibration of gold nanoparticles immersed in simple
liquids. The observed viscoelasticity is not due to molecular confinement, but is a bulk continuum effect arising
from the short time scale of vibration. This represents the first direct mechanical measurement of the intrinsic
viscoelastic properties of simple bulk liquids, and opens a new paradigm for understanding extremely high
frequency fluid mechanics, nanoscale sensing technologies, and biophysical processes.
Can we optimise the strength of porous materials?
Vivien Challis
The University of Queensland, Brisbane, QLD, Australia
email: [email protected]
The computational solution of the equations of linear elasticity leads to excellent predictions of the elastic
properties of porous and composite materials. In contrast, the failure strength of porous and composite materials
is poorly understood and is therefore difficult to predict with computational methods. I’ll overview some of
our recent work in this area. Our goal is to computationally optimise the strength of porous scaffolds for bone
replacement applications.
Mathematical Modelling of Spatial Sorting and Evolution in a Host-Parasite System
Matthew Chan
University of Sydney, NSW, Australia
email: [email protected]
Coauthors: Richard Shine, Gregory Brown and Peter Kim
There have been numerous empirical and agent-based modelling studies on the spatial self-structuring of traits,
particularly in regard to dispersal ability (termed spatial sorting) of cane toads in northern Australia and
the resultant accelerating invasion, but few mathematical modelling studies. In this study, we formulate a
reaction-diffusion based partial-integro-differential equation model based on an earlier model by Bouin et al.
(2012, Comptes Rendus Mathematique) to examine this spatial self-structuring of traits in both a cane toad
population and lungworm parasite population, which evolves with the cane toad population. In particular, the
traits we focus on are dispersal ability for the cane toad population and both prepatent period and larval size
for the lungworm parasite population. Apart from the spatial self-structuring of these traits, our results confirm
a number of observations made in empirical and agent-based studies; particularly, that there is a noticeable
lag between the host and parasite population which is critically dependent on the parasite functional response
to host densities, that older populations regress back to lower dispersal speeds and that spatial sorting can
still occur with a disadvantage in reproductivity and/or survival in more motile individuals. Moreover, we find
that such a disadvantage in reproductivity and/or survival is unlikely to be large if spatial sorting is to have
a noticeable effect on the rate of range expansion, as it has been observed to have over the last 60 years in
northern Australia.
A two-dimensional finite volume unstructured triangular mesh method for fractional-in-space
Allen-Cahn equations in irregular domains
Aimin Chen
Henan University, Kaifeng, China
email: [email protected]
Coauthors: Fawang Liu, Ian Turner, Kevin Burrage and Qianqian Yang
Fractional-in-space Allen-Cahn equations(FISAC) containing strong nonlinear source term and small perturbation shows metastability and a quartic double well potential. Using finite volume unstructured triangular mesh
method, the present paper solve the two-dimensional FISAC equations with homogeneous Neumann boundary
conditions in different irregular domains. By using linear interpolation shape function method and matrix
transfer technigues and the Lanczos interation method, the two-dimensional FISAC equations are computed
numerically on different irregular domains.
Macroscale model and boundary conditions for spring mass system with fine structure.
Chen Chen
The University of Adelaide, Adelaide, Australia
email: [email protected]
Multiscale modelling methodologies build macroscale models of materials with complicated fine structure. My
innovation is to derive correct boundary conditions to use with the macroscale model. We derive macroscopic
boundary conditions for a microscale discrete spring mass system with microscale structure. The spring mass
system has two strands and the strands are linked by springs. The derived macroscale boundary conditions
improved the accuracy of macroscale model. We verify the new boundary conditions by numerical methods.
The techniques developed here can be adapted to a range of multiscale modelling situations to provide boundary
conditions for accurate predictions.
Drawing of microstuctured optical fibres with pressurisation of the internal channels
Mike Chen
University of Adelaide, Adelaide, SA, Australia
email: [email protected]
Coauthors: Yvonne Stokes, Peter Buchak, Darren Crowdy and Heike Ebendorff-Heidepriem
Microstructured optical fibres are distinguished from solid optical fibres by the large number of internal air
channels running along their length. These fibres are manufactured by heating and stretching a preform, which
has some cross-sectional pattern of holes. In stretching the preform with a diameter of 1-3cm to a fibre with a
diameter of the order of 100 micrometers, the cross-sectional hole pattern changes in scale but is also deformed
due to surface tension. A practical way of countering this deformation is to introduce pressurisation in the
internal channels. This pressure acts against surface tension and potentially provides an extra degree of control
over the shape of the internal channel geometry. We generalise an existing model of fibre drawing to include
channel pressurisation and present examples of pressurised fibre drawing for several cross-sectional geometries
of practical importance.
Osmotically driven deformation of a stable water film
Sue Ann Chen
IBM Research, Melbourne, Australia
email: [email protected]
Coauthors: Lucy Y. Clasohm, Roger G. Horn and Steven L. Carnie
Recent experiments on a mercury drop near a mica surface show that a dimple forms on the mercury/water
interface when there is a sudden change in the electric potential of the mercury drop coated with a self-assembled
monolayer (SAM) of 11-mercapto-1-undecanoic acid thiol molecules. It is suggested that the dimple formation
is due to the desorption of a fraction of the SAM from the mercury drop surface when the surface potential is
changed. The osmotic pressure in the thin film region increases as a result of the presence of the thiol molecules
in the region, giving rise to the observed dimple. The solute concentration is introduced as a new dependent
variable in the system and the transport of the solute is described by a convection-diffusion equation. The thin
film and convection-diffusion equations form a system of coupled partial differential equations. The effects of
disjoining pressure, hydrodynamic pressure and total pressure are discussed. As the simplest version of the
model, in which desorption is assumed to be uniform and instantaneous, could not explain some features of the
experimental observations, this suggests the presence of a more refined mechanism. We explore some of the
more complicated models here.
Analysis of novel oscillations of quantized mechanical energy in mass-accreting nano-oscillator
Jeong Ryeol Choi
Department of Radiologic Technology, Daegu Health College, Daegu, Republic of Korea
Coauthors: Ji Nny Song
Quantum characteristics of mass-accreting oscillator which can be applied to analyzing quantum features of
nanomechanical mass sensing are investigated by making use of the invariant operator theory. The invariant
operator theory is one of rigorous quantum theories for dynamical systems that have time-varying parameters.
In particular, quantum energy of the system is analyzed in detail and compared it to the classical one. We
focused on two particular cases, which are linearly mass-accreting oscillator and exponentially mass-accreting
one. It is confirmed that quantum energy agrees well with the classical one in the limit h → 0 where h is the
Planck’s constant. We showed that not only the classical but also the quantum energy oscillates with time. A
reasonable explanation for this energy oscillation is given.
The influence of object shape on the convergence of active contour models for image segmentation
Josh Chopin
University of South Australia, Adelaide, South Australia, Australia
email: [email protected]
Coauthors: Hamid Laga and Stanley Miklavcic
Modern genomics experiments are often conducted in controlled environments on hundreds of plants at a time.
As such, manual and destructive phenotyping techniques are no longer suitable. Recently there has been a trend
toward automated high-throughput phenotyping facilities, in an attempt to relieve the phenotyping bottleneck.
A majority of these facilities focus on the use of cameras for non-destructive recording of plant data. Hence,
the new challenge lies in accurately segmenting the plants from 2D images in an automated manner and then
analysing structural and statistical information about them.
One such technique for image segmentation is known as the active contour model. Active contour models have
seen widespread success throughout a number of applied fields due to their versatility and semi-automated
nature. However, a high majority of these models rely on arbitrary parameters that are required to be selected
manually. Furthermore, small variations in these parameters can produce substantial variations in the method’s
overall accuracy. This makes them unsuitable for use by non-experts and also for the analysis series of images
that can change drastically over time, such as the growth of a plant.
In this talk we attempt to establish relationships between the parameter values of active contour models and
the geometry of the objects/shapes that they are segmenting. Our goal is for users to be able to utilise some
basic a-priori knowledge about the geometry of the object in order to automatically select a range of suitable
parameter values. We analyse the accuracy of active contour models over multiple series of shapes that exhibit
some pattern, such as decreasing number of sides or increasing concavity. We present a novel normalization
technique so that the parameter values are of a similar scale. We also carefully design an experimental setup
that ensures no bias between different shapes or parameter values.
We show that over a series of shapes the range of parameters that provide convergence do follow a trend. We also
show that not all contours that converge to the objects boundary do so in a stable manner, with a substantial
amount oscillating continuously. However more information, such as more shapes and more parameter values,
is required to draw meaningful and quantitative conclusions from such an analysis. Future work includes
incorporating more of this information along with the application to more active contour models. Another
exciting future direction is the use of 2D shape diagrams to quantify relationships between shapes, parameter
values and levels of accuracy.
Optimising Revenue for Concentrating Solar Thermal Power Plants with Limited Thermal Energy
Luigi Cirocco
University of South Australia, Mawson Lakes, SA, Australia
email: [email protected]
Coauthors: John Boland, Frank Bruno, Peter Pudney and Martin Belusko
The optimal control strategy for maximising of revenue for a Concentrating Solar Thermal (CST) power plant
with unlimited Thermal Energy Storage (TES) operating in an electrical energy market has been established
in our previous work where the storage state space problem was resolved using the necessary conditions of
Pontryagins Maximum Principle.
This presentation focuses on further refinements the problem where we consider the constrained storage state
using a direct adjoining technique to investigate the properties of the optimal control strategy for an extended
set of necessary conditions. We also present the development of a solution algorithm for the constrained problem
and discuss how the necessary conditions are enacted within the algorithm.
The discussion concludes with the identification of the possible refinements to the modelling and the development
of demand side models for the investigation of optimal control for electricity customers.
The Physics of Suspended Microchannel Resonators
Jesse F. Collis
The University of Melbourne, Melbourne, Victoria, Australia
email: [email protected]
Coauthors: John E. Sader
Suspended Microchannel Resonators enable mass sensing in liquid with exquisite resolution, with measurements
at the attogram level being demonstrated recently. In this talk, I will discuss our recent work on analysing the
performance of these devices using both asymptotic and numerical analyses. This work is in conjunction with
our experimental collaborators at the Massachusetts Institute of Technology (USA).
Mathematical modelling and numerical simulation of nanopores
Eamon Conway
QUT, Queensland, Australia
email: [email protected]
Coauthors: Steven Psaltis and Troy Farrell
The transport of ions through nanometre sized channels (nanopores) leads to complicated two-dimensional
behaviour due to the development of double layers at the electrode and nanopore/electrolyte interfaces. Notably,
the double layer forma- tion inside the nanopore causes selective motion, inhibiting the transport of one of the
ionic species. This behaviour, known as ion current rectification, produces an asymmetric current-voltage (I-V)
curve. We propose a mathematical model of ion transport through nanopores based on the transient PoissonNernst-Planck (PNP) equations with diffuse Butler-Volmer kinetics applied at the electrolyte/electrode interface. Such kinetics model ionic current at the working electrode. This framework allows for novel extensions
to the model, such as the inclusion of steric effects and the production of simulated I-V curves. In this talk, we
present the initial results from our proposed model.
Polar vortices on celestial bodies
Jason Cosgrove
University of Tasmania, Hobart, Tasmania, Australia
email: [email protected]
Atmospheric vortices over the polar regions of a celestial body are considered, with a particular focus on
modelling the famed North Polar Hexagon (NPH) on Saturn. The atmosphere is weakly compressible, and the
fluid motion is subject to the Coriolis pseudo-force, due to celestial bodies being in a non-inertial reference frame.
The NPH rotates in an anti-clockwise direction when viewed from above and so will be initially modelled by a
low pressure system in the form an exponential function. The standard f-plane and beta-plane approximations
are invalid over the poles and thus non-linear solutions are presented using a planar approximation where the
Coriolis parameter varies quadratically away from the pole.
Vesicle Queues: Insulin Regulation in Glucose Transport
Adelle Coster
UNSW Australia, Sydney, Australia
email: [email protected]
Mammalian cells regulate glucose levels by translocating membrane embedded glucose transporter proteins to
and from their outer cell membranes. The predominant transporter in fat and muscle cells is Glucose Transporter
4 (GLUT4) which is insulin-responsive. GLUT4 is embedded in vesicles (small spheres of membrane) for
transport. The vesicles then fuse with the destination membrane, and the GLUT4 is released.
It has been suggested that the insulin regulation of vesicle fusion is not only limiting the appearance of GLUT4
at the cell surface but also regulating the drain on internal stores, as well as the extent to which vesicles
are associated with the cell cytoskeleton. There is also evidence that the vesicles transit along microtubules
suggesting that there might be a queueing protocol for fusion.
Here, closed Markovian queueing networks with finite capacity queues are explored to determine whether the
experimentally observed features of GLUT4 translocation can be described by such systems.
Microstructure Interpolation for Macroscopic Design
Andrew Cramer
The University of Queensland, Brisbane, Australia
email: [email protected]
Coauthors: Vivien Challis and Anthony Roberts
Structural optimisation seeks to design the best possible structure for a given load case. Typically the problem
is to determine where to place a finite amount of material in a domain to minimise compliance or to maximise
stiffness under the assumption of linear elasticity. Multi-scale optimisation methods have been developed to
expand the space of allowed solutions and make use of developments in additive manufacturing. We propose a
new method of multi-scale optimisation which interpolates optimised microstructures for a material distribution
method. The technique is benchmarked against existing structural optimisation methods for some test problems.
We also discuss the benefits over existing multi-scale optimisation methods.
Elasto-plastic tissue deformations in multicellular morphogenesis
Andras Czirok
University of Kansas Medical Center, Kansas City, KS, USA
email: [email protected]
Coauthors: Dona Isai
Multicellular pattern formation is an important aspect of both embryonic development and certain pathologies
like tumor formation and invasion. Large-scale cell movements often involve cell-exerted mechanical forces
and suitably controlled changes in cell adjacency. Based on empirical data, we propose a three dimensional
mechanical model of multicellular assemblies. Mechanically coupled adherent cells are represented as particles
interconnected with elastic beams which can exert non-central forces and torques. Tissue plasticity is modeled
by a stochastic process consisting of a connectivity change (addition or removal of a single link) followed by
a complete relaxation to mechanical equilibrium. In particular, we assume that (i) two non-connected, but
adjacent particles can form a new link; and (ii) the lifetime of links is reduced by tensile forces. We demonstrate
that the proposed model yields a realistic macroscopic elasto-plastic behavior and we establish how microscopic
model parameters determine material properties at the macroscopic scale. In addition to their mechanical role,
model particles can also act as simulation agents and actively modulate their connectivity according to specific
rules. As an example, anisotropic link insertion and removal probabilities can give rise to local cell intercalation
and large scale convergent extension movements. The proposed stochastic simulation of cell activities yields
fluctuating tissue movements which exhibit the same autocorrelation properties as empirical data from avian
Geothermal Spring Temperature Analysis
Heather Davidson
Massey University, Albany, New Zealand
email: [email protected]
The aim of this study was to examine temperature time-series data recorded from several geothermal features
in the Taupo Volcanic Zone, New Zealand. Pool temperatures were recorded at 17 features at various times
between 1996 and 2011. The monitored features ranged from geysers with regular eruption cycles to hot springs
with erratic temperature cycles. The length and number of records differs for each site. The effects of rainfall,
air pressure and air temperature were analysed to ascertain whether there is a relationship between the pool
temperatures and any of these factors. Water level data from Lake Ohakuri was also examined to determine
whether it had any influence on the features at the nearby Orakei Korako geothermal area. Earlier research
on a small subset of data from the Waiotapu Geyser had found that variations in air pressure could trigger or
halt eruptions as well as affecting eruption frequency (Nikrou et al., 2013). Analysis of all available datasets
from the Waiotapu Geyser confirmed the existence of such a relationship. No other monitored features appear
to be influenced significantly by air pressure. No correlation between pool temperatures and rainfall or air
temperature were detected for any geothermal features in this study. Lake Ohakuri is part of the Waikato
River hydro scheme causing the water level to fluctuate daily. This does not appear to affect the recharge or
temperature cycles of nearby geothermal features.
Applications of Compressive Sensing
Frank de Hoog
CSIRO, Canberra, ACT, Australia
email: [email protected]
In applications it is often the case that we wish to that we wish to find an approximation to a set of linear
equations for which there are fewer equations than unknowns. In general of course this is an insoluble problem
but, if it is known that the solution can be well approximated by a sparse solution, then progress can be often
be made.
In this presentation, we briefly describe conditions under which error bounds can be established and describe
applications to which compressive sensing techniques have been applied.
The unsteady flow due to a spinning toroidal mass
Jim Denier
University of Auckland, Auckland, New Zealand
email: [email protected]
Coauthors: Sophie Calabretto and Trent Mattner
The flow due to a rotating torus provides a paradigm for the study of many phenomena that arise in unsteady
fluid flows. It also provides a model for the flow induced by the colelctive motion of fish contained within an
aquaculture pen. This talk will present some new results demonstrating that this flow evolves through a series
of well defined stages, starting from a collision of viscous boundary layers which result in the development of
a radial jet. This radial jet is preceded by a starting vortex which subsequently detaches forming an isolated
toroidal vortex. The radial jet then develops an absolute instability which leads to a turbulent flow in the
vicinity of the sphere’s equator. In the context of the collective motion of fish contained in aquaculture pens,
the fluid flow they induced would serve to provide an induced force which would impact upon the overall pen
structure. Such interactions are observed as a draw-up of the aquaculture pen.
Mathematical modelling of atherosclerosis - atheoma plaque formation, development and rupture
Yan Ding
RMIT University, Melbourne, Victoria, Australia
email: [email protected]
Coauthors: John A. Gear
Atherosclerosis is a medical terminology meaning artery hardening. It is resulted by the presence of fatty
deposits, such as low density lipoprotein (LDL), monocytes and macrophages, etc. accumulated in the walls of
the arteries, which results thickening the artery wall, narrowing the passageway of the blood flow and leading
to a reduction in the blood flow through the blood vessels. This process is called plaque formation. The initial
stage of a plaque build-up in an artery wall is asymptomatic. However, as a plaque grows, the blockage of
blood flow becomes severe. In some serious cases, a plaque is ruptured, which releases thrombogenic agents into
the blood stream resulting fatal damage. Atherosclerosis occurring in different areas of the body has different
effects. In the brain, atherosclerosis would cause thrombus, meaning oxygen is being cut off from the brain,
leading to brain damage and stroke. In the aorta, plaque building-up would cause artery wall rupture due to
the ballooning of the artery wall. Atherosclerosis in legs would decrease blood circulation, and in serious cases,
amputations may be the only option to save the lives. Thrombosis would occur in coronary arteries, causing
heart attack. Atherosclerosis is, in fact, the main contributor to myocardial and cerebral infarctions, which had
been linked to 50% of all fatality across USA, Europe and Japan in 1990’s. According to the fact sheet No317
of the World Health Organization (WHO), released in March 2013, cardiovascular disease (CVD), mainly from
heart disease and stroke, are the first leading cause of death globally; and the number of death will reach 23.3
million by year 2030.
The initiation and progression of atherosclerosis involve many biomedical and biochemical aspects. In this
presentation, we report our current research activities and achievements in the mathematical modelling of the
complex phenomenon. We also discuss the main objectives of the research and present our frame work for
achieving these objectives.
Quantifying spatial distributions using a pair correlation function based on generalized measures
of separation
Saber Dini
The University of Adelaide, Adelaide, SA, Australia
email: [email protected]
Pair correlation functions are statistical tools for analyzing spatial distributions. They describe the frequency
of distances between pairs of data points. Pair correlation functions have been used to analyze the distributions
of objects in various fields, from the stars in the galaxy to cells in a dish. In this talk, we derive a pair
correlation function based on a generalized distance obtained by projecting the positions of points from a higher
dimensional space into a one dimension (this includes the Euclidean distance but also e.g. angular separation).
By using the features of order statistics on the distribution of generalized distances, we are able to estimate the
expected value of the frequency of pairs for objects distributed with a given probability density function. We
can thus normalize an observed distribution of interest relative to any reference distribution (which need not
be uniform), which allows us to analyze the deviation of the data from this reference distribution. We present
preliminary results of applying our method to analyze experimental data concerning the distribution of cells
within spheroids.
Accurate Approximations of the Riemann-Stieltjes Integral
Silvestru Sever Dragomir
Victoria University, Melbourne, Victoria, Australia
email: [email protected]
Riemann-Stieltjes integral for complex or real-valued functions plays a key role in various fields of Mathematics,
including Probability Theory & Statistics, Complex Functions Theory, representation of selfadjoint operators
on complex Hilbert spaces, in Numerical Analysis and for Quadrature rules etc.
In this presentation we survey some recent inequalities of Ostrowski, Trapezoid and Gruss type for RiemannStieltjes integral obtained by the author and show how these can be used to provide accurate quadrature rules
in approximating the Riemann-Stieltjes integral.
A hybrid higher-order numerical scheme for convection-diffusion problems
Jerome Droniou
Monash University, Clayton, VIC, Australia
email: jero[email protected]
Coauthors: Daniele Di Pietro and Alexandre Ern
Convection-diffusion equations permeate a variety of fluid flows models, including in particular flows in porous
media. In such models, the natural diffusion can be in some places much smaller than the convection driven
by the Darcy velocity, and it is therefore essential to dispose of numerical methods that can automatically and
locally adapt to the flow regime (diffusion-dominated or convection-dominated). Some practical constraints
must also be taken into account, such as e.g. the capacity for the method to be efficiently implemented in a
parallel environment.
In this talk, we will present a numerical scheme of arbitrary order to deal with convection-diffusion equations.
This scheme uses separate degrees of freedom on cells and faces, and has a local connectivity (each cell is only
connected to its faces) which makes it a good candidate for parallel implementations. The discretisation of the
convective terms uses a stabilisation which automatically adjusts to all regimes (including vanishing viscosity).
I will also present error estimates which are optimal in all regimes, thanks to the usage of local P´eclet numbers.
Making Waves: High Frequency Volatility Estimation and the Hilbert-Huang Transform
Carson Drummond
University of Wollongong, Wollongong, NSW, Australia
email: [email protected]
In this presentation a new way to estimate the spot volatility of high frequency foreign exchange data using
the Hilbert-Huang transform is introduced. The proposed volatility estimate was designed to overcome the
difficulties encountered when microstructure noise is present. The problem of assessing the validity of latent
variable estimates is overcome by setting up a virtual options trading market in which competing volatility
forecasts buy and sell straddle options to one another using real high frequency foreign exchange data.
Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules
for Key Transport Modes.
Michelle Dunbar
University of Wollongong, Wollongong, NSW, Australia
email: [email protected]
As the population within modern metropolitan cities continues to grow, greater population dispersion means
that daily commuters are increasingly faced with longer commute times and journeys consisting of multiple
legs; often involving more than one mode of transport. In a bid to discourage the use of the private motor-car
and facilitate the uptake of public transport, there is a developing trend towards the construction of centrallylocated Transport Hubs, allowing passengers to connect with multiple modes of transport. To assist passengers in
connecting with their outbound mode more efficiently, it is desirable to synchronise connecting modal services
within the Transport Hub. In this presentation we consider the problem of designing shuttle-bus routes for
passengers connecting with one of four different modes of transport at a Transportation Hub. We seek to
minimise the average waiting time for passengers, the cost of missed connections at the Hub and the total travel
time. Furthermore, we incorporate time-of-day effects and passenger heterogeneity with respect to value-oftime. In addition to commuters, the framework developed is amenable and directly extensible to the perishable
good delivery problem for which items possess heterogeneity in delivery priority. Our model is posed as an
extension of the vehicle routing problem with time windows, and solved using column generation. We provide
a brief outline of our optimisation formulation and preliminary results for a number of datasets.
Modelling of graphene oxide and carbon nanotubes in a nematic liquid crystal using continuum
Tom Dyer
University of Wollongong, NSW, Australia
email: [email protected]
Coauthors: Ngamta Thamwattana
In this study, we construct a continuum model for graphene oxide based upon the Lerf-Klinowski structure to
investigate the idea of liquid crystal dispersions. We use the Lennard-Jones potential and Coulombs law to
determine the potential energy between sheets of graphene oxide. Our model is then modified to investigate
different levels of hydration and oxidation within the system. We find that the results discovered using the
continuum approach match experimental results found in literature. This model is then used to explore the idea
of liquid crystal constructions of graphene oxide and nanotubes, where the tubes and sheets prevent each other
from aggregation. We investigate the orientation and position of a single-walled carbon nanotube between our
sheets of graphene oxide at equilibrium. We find that sufficiently short nanotubes prefer to orient perpendicular
between the sheets. Additionally, the nanotubes do not form bundles and instead form some alignment. Our
investigations are reconstructed using the LAMMPS molecular dynamics simulations and we compare them
with our mathematical modelling results.
Symmetry, Invariance and Criticality
Andrew Eberhard
RMIT University, Melbourne, Australia
email: [email protected]
Coauthors: Vera Roshchina
The aim of this talk is to summarise, relate, explain and generalise a range of results in nonsmooth, and
predominantly nonconvex analysis, that exploit the symmetry of underlying problems. Results of this kind date
back to the work of Palais on the principle of symmetric criticality but there more recent results that can be
placed in a similar framework. We will discuss some old and new results.
Characterising transport through a crowded environment with different obstacle sizes.
Adam Ellery
Queensland University of Technology, Brisbane, QLD, Australia
email: [email protected]
Coauthors: Matthew Simpson, Scott McCue and Ruth Baker
Transport through crowded environments is often classified as anomalous, rather than classical, Fickian diffusion.
Several studies have sought to describe such transport processes using either a continuous time random walk
or fractional order differential equation. For both these models the transport is characterized by a parameter
α, where α = 1 is associated with Fickian diffusion and α < 1 is associated with anomalous subdiffusion. Here,
we simulate a single agent migrating through a crowded environment populated by impenetrable, immobile
obstacles and estimate α from mean squared displacement data. We also simulate the transport of a population
of such agents through a similar crowded environment and match averaged agent density profiles to the solution
of a related fractional order differential equation to obtain an alternative estimate of α. We examine the
relationship between our estimate of α and the properties of the obstacle field for both a single agent and a
population of agents; we show that in both cases, α decreases as the obstacle density increases, and that the rate
of decrease is greater for smaller obstacles. Our work suggests that it may be inappropriate to model transport
through a crowded environment using widely reported approaches including power laws to describe the mean
squared displacement and fractional order differential equations to represent the averaged agent density profiles.
The Complexity of Optimal Experimental Design: A Tour from Applied Probability to Experimental Mathematics
Ali Eshragh
The University of Newcastle, Newcastle, NSW, Australia
email: [email protected]
In this presentation, we deliver our theoretical and numerical results on the Fisher Information for the birth
rate of a partially-observable simple birth process involving n observations. Our goal is to estimate the rate
of growth, λ, of a population governed by a simple birth process. We may choose n time points at which to
count the number of individuals present, but due to detection difficulties, or constraints on resources, we are
able only to observe each individual independently with fixed probability p. We discuss the optimal times at
which to make our n observations in order to maximize the Fisher Information for the birth rate λ. Finding
an analytical form of the Fisher Information in general appears intractable. Nonetheless, we find a very good
approximation for the Fisher Information by exploiting the probabilistic properties of the underlying stochastic
process. Both numerical and theoretical results strongly support the latter approximation and confirm its high
level of accuracy. However, this approximation is limited to the number of observations. Eventually, we utilized
techniques from Experimental Mathematics to calculate the Fisher Information efficiently.
An Investigation into Probabilistic Constraint in Optimal Power Flow Model
Soorena Ezzati
Federation University, Ballarat, Victoria, Australia
email: [email protected]
Coauthors: Musa Mammadov and Sid Kulkarni
There are many accepted optimisation models available for electricity distribution networks and one of these
models is optimal power flow (OPF). The main objective of an OPF model is to minimise total cost (including
manufacturing, instalment and maintenance costs) of an electricity network. Safety is one of the most challenging
aspects of designing electricity networks. Although several reliability indices are introduced in the literature to
take into account uncertainties, there is no probabilistic constraint/model for these networks. In this paper,
we introduce a safety condition for an electricity network based on the existing constraints in the related
OPF model. This condition will then be used to formulate a performance function for the electricity network.
A probabilistic constraint is introduced using the defined performance function to keep failure probability of
the network below than a predetermined accepted level. It’s anticipated to experience an extra cost while
the probabilistic constraint is introduced. A non-deterministic optimisation problem must be formulated to
minimise the extra cost which is experienced by considering network reliability using probabilistic constraint.
Modeling the care pathway for stroke patients
Mark Fackrell
University of Melbourne, Melbourne, Victoria, Australia
email: [email protected]
Coauthors: Ria Szeredi and Peter Taylor
When patients who have suffered a stroke present at a hospital emergency department, depending on the
severity, it is vital that they are seen and treated quickly so that their health outcomes are optimal. In this talk
we will analyse and discuss the care pathway for stroke patients at a major metropolitan hospital. We establish
that while the number of stroke arrivals each day is distributed according to a Poisson distribution, the arrival
process is not Poisson. Also, we fit phase-type distributions to the length of stay in hospital of stroke patients,
which yields some interesting results.
GPU accelerated algorithms for computing matrix function vector products
Megan Farquhar
Queensland University of Technology, Brisbane, Queensland, Australia
email: [email protected]
Coauthors: Timothy Moroney, Qianqian Yang and Ian Turner
Recently, there has been increased interest in the use of fractional diffusion models in many applications.
Computing the numerical solution of these models often requires the computation of a matrix function vector
product involving a sparse matrix raised to a fractional power. The fractional power arises as a result of the nonlocal nature of the operator, and motivates numerical methods that avoid the direct computation and storage of
the resulting dense matrix . In this talk we introduce methods for computing matrix function vector products
such as these that take advantage of GPU acceleration. The introduction of GPU-accelerated techniques results
in improved computational times compared to CPU-only algorithms.
We use a contour integral approach that transforms the computation of matrix function vector products into
the sum of weighted shifted linear system solves. We improve the convergence of our methods and thereby
significantly reduce device memory overheads by introducing two levels of preconditioning. We demonstrate the
effectiveness of our approach by presenting results that demonstrate an order of magnitude speed up. We also
show how the method can be used to efficiently compute numerical solutions to a fractional diffusion equation.
Periodically forced circulation near the shore of a lake
Duncan Farrow
Murdoch University, Murdoch WA, Australia
Approximate analytical and numerical solutions for a model of the near-shore circulation in a lake subject to two
diurnal forcing mechanisms are presented. The first mechanism is a heating/cooling term in the heat equation
representing the daytime heating and nighttime cooling of the diurnal cycle. The second is a periodic surface
stress modelling a sea-breeze/gully wind system typical of some coastal regions. The two forcing mechanisms
can either act together or against each other depending on their relative phase. When the forcing mechanisms
are opposed and of sufficient strength unstable density profiles lead to secondary circulation.
Existence Results for the Thomas–Fermi model of the atom with Bohr boundary conditions.
Nick Fewster-Young
UNSW Australia, Sydney, NSW, Australia
email: [email protected]
In 1927, L. H. Thomas and E. Fermi derived a nonlinear differential equation that models the electrical potential
in an atom under varying conditions. This talk investigates the instance when the atom is neutral; presenting
novel existence results concerning the theory and a numerical approximation to a solution. The results complement and extend on the work of R. Agarwal and D. O’Regan in Singular Differential Equations. Also, the work
aligns with the computation methods derived by C. Chan and Y. Hon for a numerical solution in 1988. The
methods used are differential inequalities to yield a priori bounds on possible solutions and toplogical methods
to prove the existence results.
Patient Flows and Markov Decision Processes
Jerzy Filar
Flinders University, Adelaide, Australia
email: [email protected]
Coauthors: Anthony Clissold
While the flow of patients in a hospital is a complex stochastic process, bed occupancy data exhibit characteristic
regularities that lend themselves to quantitative modelling. In this study midnight census data from a three
year period at Flinders Medical Centre (FMC) were used to develop a coarse Markov Decision Process (MDP)
model whose steady state behaviours were in general concordance with the observed data under the “business
as usual” scenario. Of course, the model also included multiple, possible, actions to alleviate congestion, from
which alternative operating scenarios could be derived. The model and some of its findings will be briefly
described in this presentation.
Spatiotemporal mathematical modelling of mutations of the dhps gene in African Plasmodium
falciparum malaria
Jennifer Flegg
Monash University, Melbourne, Australia
email: [email protected]
Plasmodium falciparum malaria has repeatedly evolved resistance to antimalarial drugs, thwarting efforts to
control and eliminate the disease and contributing to an increase in mortality. In this talk I will discuss a
mathematical model developed to map the spatiotemporal trends in the distribution of mutations in the dihydropteroate synthetase (dhps) gene that are highly correlated with resistance to sulphadoxine-pyrimethamine
(SP). The aim of this work was to present a proof of concept for spatiotemporal modelling of trends in antimalarial drug resistance that can be applied to monitor trends in resistance of other antimalarials, as they
emerge or spread.
Prevalence data of single nucleotide polymorphisms in three codon positions of the dhps gene from published
studies across Africa were used within a geostatistical model to create predictive surfaces of the dhps540E
mutation over the spatial domain of sub-Saharan Africa from 1990-2010. The statistical model was implemented
within a Bayesian framework and quantified the associated uncertainty of the prediction of the prevalence of
the dhps540E mutation in sub-Saharan Africa.
The maps presented visualize the changing prevalence of the dhps540E mutation in sub-Saharan Africa. These
allow prediction of space-time trends in the parasite resistance to SP, and provide probability distributions of
resistance prevalence in places where no data are available as well as insight on the spread of resistance in a
way that the data alone do not allow. The results of this work will be extended to design optimal sampling
strategies for the future molecular surveillance of resistance, providing a proof of concept for similar techniques
to design optimal strategies to monitor resistance to ACT.
What is Fluid Turbulence?
Larry Forbes
University of Tasmania, Hobart, Tasmania, Australia
email: [email protected]
Modelling turbulent fluid flow remains one of the difficult unsolved problems of classical mechanics. An enormous
amount of work has been done on this over the past century, and much is known about the phenomenon
experimentally. There are also many computer codes that account for turbulence, usually based on heuristic
models involving somewhat arbitrary closure assumptions.
Although it is usually stated that turbulence is governed by the Navier-Stokes equations, these equations do
not predict the transition to turbulent flow correctly, nor are they used exactly in computer codes for turbulence. This talk examines the alternative hypothesis that turbulence is, in fact, a manifestation of weakly
non-Newtonian behaviour. The difference from Navier-Stokes theory is discussed, and the transition to turbulence is investigated. The aim is to obtain a more coherent account of the underlying physics.
Residence-Time Distribution of Heaped and Sloped Powder Layers in a Conical Mass-Flow Hopper
Luke Fullard
Massey University, Palmerston North, New Zealand
email: [email protected]
Coauthors: Clive Davies and Sam Irvine
The flow of a hypothetical Coulomb material flowing under gravity from a conical mass-flow hopper is modelled
using stress field theory. The assumptions inherent for a Coulomb material can be combined with the assumption
of radial flow within the hopper to determine the velocity profile within the hopper. From the velocity profile,
ejection times and residence time distributions may be calculated. Since, in a real granular system, the powder
layer interface is generally not flat, but sloped at some angle, (nominally the angle of repose), the residence
time distribution and ejection times will be dependent on the initial geometry of the powder layers. Residence
time distributions and ejection times are calculated for a given granular material in a conical mass-flow hopper
firstly for the case of flat layers, secondly for the case where the powder forms a conical heap at the angle of
repose, and thirdly for the case when the powder is sloping against a wall. It is found that the shape of the
powder layers greatly changes the residence time distribution and ejection times in the system, and needs to be
considered when performing residence time measurements in the industrial setting.
Achilles tendon turnover and adaptive remodelling
Bruce Gardiner
The University of Western Australia, Crawley, WA, Australia
email: [email protected]
Coauthors: Stuart Young, Arash Mehdizadeh, Jonas Rubenson and David Smith
A mathematical model of Achilles tendon damage, repair and adaption in normal daily activity is proposed.
Key aspects of the model include (1) reproducing the non-linear stress-strain behaviour of tendon based on
a distribution of collagen fibre lengths, (2) a stochastic model of individual fibre mechanical and proteolytic
damage and cell-mediated repair based on known biology, and (3) incorporating the tendon model into a multitimescale model of the muscle-tendon unit. Tendon efficiency is assessed using metabolic energy costs. With
this model, the predicted tendon remodelling, based on individual fibre damage and repair, is found to minimise
metabolic costs of the tendon. That is, physical activity causing mechanical damage and repair to tendon fibres
leads to shifts in the fibre length distribution and overall efficiency of the muscle-tendon unit. Conversely a lack
of physical activity leads to reduction of tendon metabolic efficiency due to a reduced mechanical damage, but
increased proteolytic damage. The proposed model therefore provides a framework for understanding the role
of physical activity in tendon health and adaption.
A modification to the component-by-component construction that simultaneously chooses the
Alexander Gilbert
University of New South Wales, NSW, Australia
email: [email protected]
Coauthors: Frances Kuo and Ian Sloan
We present a novel modification of the component-by-component (CBC) algorithm for choosing the generating
vector of a rank-1 lattice rule that simultaneously chooses the optimal weights. Assuming that a bound on
the norm of the integrand is known we use a simple minimisation to obtain a formula for the weight in each
dimension. Numerical results are also provided.
Impact of delta hepatitis on hepatitis B epidemiology and optimal intervention policies
Ashish Goyal
The University of NSW, Sydney, Australia
email: [email protected]
Coauthors: John M. Murray
The major cause of liver cancer around the globe is hepatitis B virus (HBV) which also contributes to a large
number of deaths due to liver failure. Hepatitis delta virus (HDV) is as potentially alarming as HBV since life
threatening cases are 10 times more likely with HBV-HDV dual infection as compared to HBV mono-infection.
Quantitative modelling can lead to a better understanding of HDV epidemiology and health policies to reduce
its impact.
Numerous studies have captured the transmission dynamics of HBV in a population, including determining
optimal controls to curb HBV. However the impact of HDV has not been considered. Therefore, we construct a
mathematical model to represent the transmission of HBV and HDV, and compare both the health benefit and
cost outcomes of four interventions: testing with HBV adult vaccination (diagnosis), diagnosis with antiviral
treatment for HBV mono-infected individuals, diagnosis with antiviral treatment for dually infected individuals
and awareness programs.
We find that the presence of HDV makes little difference to the structure of optimal control policies. However,
HBV prevalence, HDV prevalence, the cost per capita at 50 years and the death toll all increase significantly
in moderate and high HDV endemic regions compared to HBV mono-infected regions. Modelling also showed
that in highly HDV endemic countries with poor infrastructure, high efficacy awareness programs can be used
as a substitute for high cost antiviral treatment. These results can assist policymakers.
Bootstrapping methods for prediction intervals for solar radiation forecasts
Adrian Grantham
University of South Australia, Adelaide, South Australia, Australia
email: [email protected]
Coauthors: Yulia Gel and John Boland
We first develop a forecasting method to forecast one step-ahead hourly solar global horizontal irradiance.
Fourier analysis is used to identify any periodicity in the series and then an autoregressive model is used to
identify any serial correlation in the time series.
The residuals are then placed into a 2-dimensional matrix according to the sun elevation and solar hour angle.
The rows correspond to sun elevations in increments of 10 degrees and the columns correspond to solar hour
angles in increments of 15 degrees. This takes care of the systematic variation in variance in the time series.
We then generate N synthetic forecasts by using a bootstrapping technique. For each hour, a residual is randomly
sampled (with replacement) from the 2-dimensional matrix, according to the sun’s elevation and hour angle,
and is added to the forecast to generate a synthetic value.
Then for each hour, the 2.5 and 97.5 percentile from the N synthetic forecasts are calculated. This provides
the lower and upper prediction intervals respectively in which 95% of the forecasts will lie. We then compare
this bootstrapping method to another method where the prediction intervals are generated using the percentiles
from the residuals in the 2-dimensional matrix. We chose the simpler and more efficient percentile method for
generating prediction intervals.
It’s not just what you do, it’s where you do it: Signalling through Akt
Catheryn Gray
University of New South Wales, NSW, Australia
email: [email protected]
Coauthors: Adelle Coster
Akt/PKB (protein kinase B) is a key biochemical regulator within mammalian cells. It is a switch-point for
numerous signalling pathways that display distinct signalling modalities. One of these key pathways is the
regulation of glucose transport by insulin. The phosphorylation (activation) of only a small percentage of the
Akt pool in insulin-sensitive cells results in maximal activation of downstream components: it is a very low
threshold switch.
Akt is phosphorylated at the plasma membrane (PM) but is found in the phosphorylated state both at the
PM and in the cytosol. Recent experimental evidence suggests that the physical location of Akt, and not
just its phosphorylation state, is an important determinant of downstream regulation. Here we present an
experimentally validated four compartment model of Akt activation and its effect on some of its downstream
components in the insulin signalling pathway.
Mathematical models for cell-extracellular matrix interactions in tissue development
Edward Green
University of Adelaide, SA, Australia
email: [email protected]
Tissue engineers hope in future to be able to grow functional tissues in vitro to replace those that are damaged
by injury, disease, or simple wear and tear. Many cell culture methods involve seeding cells within gels such as
collagen, designed to mimic the cells’ environment in vivo. Amongst other factors, it is clear that mechanical
interactions between cells and the extracellular matrix (ECM) in which they reside play an important role in
tissue development. This talk presents a mathematical model which explores the role played by the anisotropic
mechanics of the ECM in shaping the form of tissues grown in vitro.
Modelling Surtseyan Ejecta
Emma Greenbank
Victoria University, Wellington, New Zealand
email: [email protected]
Coauthors: Mark McGuinness
Surtseyan Ejecta are formed in shallow sub-aqueous eruptions. They occur when water containing sediments,
or sediments saturated with water, sink, as a mud, into the magma during an eruption and are ejected from
the volcano in a ball of magma. After ejection there is a large temperature gradient between the magma at
approximately 1000 ◦ C and the mud at 20 ◦ C. As the temperature of the mud increases the water, in the mud,
evaporates causing the pressure to increase until either the pressure exceeds the tensile strength of the magma,
causing an explosion, or the water source is depleted due to the steam escaping through the magma. The
volcanological question is whether the ball of magma ruptures. There is evidence of intact ejecta so we can
conclude it does not always occur. I am developing a set of equations that accurately and transiently model
the changes in temperature and pressure in surtseyan ejecta. These equations are then used to predict the
conditions needed for an explosion to occur. In my presentation I will share some of the progress I have made.
Nonparametric comparison of regression surfaces to assess the impacts of vegetation re-growth
on wind fields
Rachael Griffiths
University of New South Wales, Canberra, Australia
email: [email protected]
Bivariate distributions representing the wind direction response to changing prevailing wind conditions can be
empirically estimated from discrete data using a variety of methods, including thin-plate-smoothing splines.
These distributions are presented here as regression surfaces over the torus and a statistical test for equality
between two surfaces is constructed. The Wild bootstrap algorithm is implemented to construct the distributions
of two test statistics based on (1) the difference between the two estimated surfaces and (2) the difference between
each surface and the surface constructed from the combined dataset. A comparison of wind response surfaces
is used to investigate whether vegetation re-growth has a significant impact on wind behaviour across complex
Stretching viscous threads
Bronwyn Hajek
University of South Australia, SA, Australia
email: [email protected]
Coauthors: Yvonne Stokes and Jonathan Wylie
The drawing of optical fibres is an important example of a viscous extensional flow where an axisymmetric
viscous thread is pulled at its ends. Other examples include the drawing of glass and polymer fibres for
optical microscopy and for glass microelectrodes. Using a one dimensional model, we examine the evolution of
axisymmetric viscous threads of various initial shapes that are pulled from both ends with a prescribed velocity
which may vary with time. We find asymptotic expressions for the evolving thread shape, both when inertia
is small, and when inertia becomes important at large times. Both the small inertia solutions and large time
asymptotic expressions compare well with numerical solutions.
Applying Polynomial Chaos to Epidemic Models
David Harman
Griffith University, Brisbane, Australia
email: [email protected]
Coauthors: Peter Johnston
Epidemic Models constructed using compartment models consisting of systems of ordinary differential equations
are widely used and studied. However, the parameters within these models, as well as their initial conditions,
are rarely known with accuracy. It is important to include the uncertainty in these parameters and initial
conditions into our model or our model may give misleading results.
Generalised Polynomial Chaos (gPC) is a new method that incorporates the probability distribution of these
parameters and initial conditions directly into the model. gPC involves two different methods: stochastic
Galerkin and stochastic collocation. The stochastic Galerkin method expands the solution as the sum of
deterministic solutions multiplied by orthogonal polynomials from the Askey Scheme, where the weight function
of the orthogonal polynomials matches the probability density function of the parameters. The stochastic
collocation method evaluates the model at specific nodes (which are the roots of the orthogonal polynomials used
in the stochastic Galerkin method) and multiplies these node evaluations by predetermined weights. From both
the stochastic Galerkin and stochastic collocation methods, the mean and variance can easily be determined.
gPC has many advantages over existing methods, such as Monte Carlo sampling. gPC is much less computationally expensive. Additionally, once gPC has been applied to the model, the parameter values and initial
conditions can easily be adjusted without having to rederive the gPC equations.
During my talk, I will look briefly at the gPC method and its applications to epidemic modeling. I will then
compare the solutions found with gPC with Monte Carlo sampling as well as the time taken to determine each
Mixed-Mode Oscillations and Canard orbits in Chemical Oscillators
Cris Hasan
University of Auckland, Auckland, New Zealand
email: [email protected]
Coauthors: Hinke Osinga and Bernd Krauskopf
A mixed-mode oscillation (MMO) is a complex waveform with a pattern of alternating small- and largeamplitude oscillations. MMOs have been observed experimentally in many physical and biological applications,
but most notably in chemical reactions. We are interested in MMOs that appear in chemical systems with one
fast and two slow variables. The presence of slow and fast epochs in such systems provides a mechanism for
generating small and large oscillations. The mathematical analysis of MMOs is very geometric in nature and
based on singular limits of the time-scale ratios. Near the singular limit one finds so-called slow manifolds that
guide the dynamics on the slow time scale. In systems with one fast and two slow variables, slow manifolds are
surfaces that can be either attracting or repelling. Transversal intersections between attracting and repelling
slow manifolds are called canard orbits. Our aim is to analyse how slow manifolds and canard orbits organise
the patterns of MMOs in a model of an autocatalytic chemical reaction.
A new closed-form formula for pricing European options under a skew Brownian motion
Xin-Jiang He
University of Wollongong, Wollongong, NSW, Australia
email: [email protected]
Coauthors: Song-Ping Zhu
In this paper, we present a new pricing formula based on a modified Black-Scholes model with the standard
Brownian motion being replaced by a special type of skew Brownian motions. In particular, the adopted
stochastic process for the dynamics of the underlying asset is the sum of a standard Brownian motion and a
reflected Brownian motion that are independent of each other. The motivation for such a modification originates
from observations of the non-normal distribution of asset log-price in the financial markets (see Peiro(1999),
Rachev(2005), Kim(1999)), which are at odds with one of the fundamental assumptions in the Black-Scholes
pricing theory. Although Corns & Satchell(2007) have worked on this model, the results they obtained are
incorrect. In this paper, not only do we identify precisely where the errors in Corns & Satchell(2007) are,
but also present a new closed-form pricing formula based on a new equivalent martingale measure. The newly
derived option pricing formula takes the Black-Scholes formula as a special case and it does not add any
significantly extra burden in terms of numerical computations involved in calculating option values, compared
with those involved in invoking the Black-Scholes formula. Amazingly, the simple analytic form of the BlackScholes formula is preserved by the new formula and an elegant financial interpretation can also be given under
the new martingale measure.
Mobile kangaroo to sedentary Abalone - what scale to manage?
John Hearne
RMIT University, Melbourne, Vic, Australia
email: [email protected]
We consider two species of contrasting mobility: sedentary abalone and free-roaming kangaroo. Abalone are
managed at a zone level while commercial divers are profit-driven and make decisions regarding where to harvest
at a reef level. What are the implications of this? It is claimed that kangaroo cannot be commercially ‘farmed’
as they are not constrained by standard fencing practices. They roam freely amongst different properties
according to the availability of forage. Can a property owner manipulate matters to benefit from harvesting
animals that have been raised largely on a neighbour’s property? Differential equation models of these systems
will be formulated and analysed. Some results will be presented that yield some insights into these issues and
the appropriate scale of management.
A model of Ebola for evaluating control
Roslyn Hickson
IBM Research, Australia, Australia
email: [email protected]
Coauthors: Emma McBryde, Rob Moss, Nicholas Geard and Matthew Davis
The recent outbreak of Ebola in Western Africa has infected an estimated twenty thousand people so far, with
approximately eight thousand deaths. This outbreak has highlighted the importance of a strong healthcare
system, with beds in isolation units, home isolation, and the important role of healthcare workers in stopping an
epidemic. We have formulated a model of Ebola Virus Disease to consider these effects, with spatial components
incorporated through a metapopulation model. We demonstrate possible results of control strategies in Western
Africa, using the Spatio-Temporal Epidemiological Modeler (STEM).
Washing sugar pulp with dirty maths.
Graeme Hocking
Maths & Stats, Murdoch University, Western Australia, Australia
email: [email protected]
Sugar pulp (Megasse) is flushed of the sugar it contains as it moves along a conveyor by cycling water through
a system of sprinklers and collectors. The unit is completely enclosed and is therefore difficult to monitor for
water level, overflow or drying. A patchwork of mathematical techniques is used to set up a very simple model
to monitor the situation in real time. This was a problem at the 2014 Mathematics-in-Industry Conference in
Johannesburg, South Africa. Some general management advice can be given from the simple model.
Exploring bifurcations and seasonality in a mathematical model of childhood disease
Alexandra Hogan
The Australian National University, Canberra, ACT, Australia
email: [email protected]
Coauthors: Kathryn Glass, Hannah Moore and Bob Anderssen
Respiratory syncytial virus (RSV) is the main cause of acute lower respiratory tract infections in infants and
young children, with almost all children infected by the age of two. Because of the significant health care and
economic burden of RSV, an improved understand of its transmission dynamics will benefit health care and
vaccination planning.
In temperate climates, RSV dynamics are highly seasonal, with mid-winter peaks and low incidence during the
summer months. While the dynamics of RSV infection are quite complex, we show that they can be captured
by an ordinary differential equation model with sinusoidal forcing.
Using parameter values derived from fitting the model to population-linked laboratory data for Western Australia, numerical bifurcation and phase plane analyses are presented that demonstrate the range of different
seasonal patterns that the model can reproduce. Based on this analysis, we suggest possible drivers of the
different seasonal patterns observed globally, and discuss the next steps for this research.
The interaction of acidic tumours and chemotherapy
Andrew Holder
University of Wollongong, Wollongong, NSW, Australia
email: [email protected]
Coauthors: Marianito Rodrigo
Tumour development is a complex process with many well observed yet poorly understood processes. As such
there are many opportunities for mathematics to help contribute to this field of research. One such process
with this potential is aerobic glycolysis.
Aerobic glycolysis or the “Warburg Effect” is a type of metabolism that the vast majority of tumours possess.
While the physical process of aerobic glycolysis is well understood, the reasons that tumours acquire this
mechanism are still debated. A consequence of aerobic glycolysis is the production of excess protons that result
in the acidification of the tumour microenvironment. This acidic environment is inhospitable to normal cells
and as such results in normal cell death. It is therefore proposed that this acidification provides a mechanism
for invasion known as the acid-mediation hypothesis. This hypothesis has been examined so far as a relatively
closed system, in that very few external influences, such as a treatment, have been considered. As such, I have
considered a model for acid-mediated tumour invasion with chemotherapy intervention.
In this talk I will provide a brief explanation of the acid-mediation hypothesis and will present the results obtained from the analysis of the model that considers the interaction between an acidic tumour and chemotherapy
Asymmetries in the distribution of gene expression noise direct spatial organization in the developing mammalian embryo
William Holmes
University of Melbourne, Melbourne, VIC, Australia
email: [email protected]
A critical event in early mammalian embryo development is robust construction of a pluripotent inner cell mass
surrounded by a trophoectoderm. Here, we utilize multi-scale, spatial stochastic modeling in conjunction with
quantitative immunofluorescence imaging to uncover the design principles responsible for robust establishment
of blastocysts. Results show that by controlling the timing and pace of cell fate specification, the embryo creates
a crucial window of time where noise in gene regulation promotes accurate organization of these multicellular
structures. Imaging results further indicate different gene products (Oct4 and Cdx2) exhibit significantly different levels of noise variation. Surprisingly, this asymmetry is functional and provides a novel means to balance
the positive and negative influence of stochasticity on organization. More generally, these results suggest noise
has a crucial positive role in spatial organization, and that levels of stochasticity may be tuned much like
expression levels themselves.
On the Euclidean Dimension of Graphs
Jin Hyup Hong
Great Neck South High School, Great Neck, USA
The Euclidean dimension of a graph G is defined to be the smallest integer d such that the vertices of G can
be located in Rd in such a way that the two vertices are unit distance apart if and only if they are adjacent
to G. In this paper we determine the Euclidean dimension for twelve well-known graphs. Five of these graphs,
urer, Franklin, Desargues, Heawood and Tietze can be embedded in the plane, while the remaining graphs,
atal, Goldner-Harrary, Herschel, Fritschr, Gr¨otzsch, Hoffman and Soifer have Euclidean dimension 3. We
also present explicit embeddings for all these graphs.
A comparison of computational techniques of the key properties of Markov Chains
Jeffrey Hunter
Auckland University of Technology, Auckland, New Zealand
email: [email protected]
The presenter has recently been exploring the accurate computation of the stationary distribution for finite
Markov chains based upon the Grassman, Taksar and Heyman (GTH) algorithm ([1]) with further extensions of
this procedure, based upon the ideas of Kohlas ([2]), for finding the mean first passage time matrix. The methods
are numerically stable as they do not involve subtraction. In addition, a number of perturbation techniques,
where the rows of the transition matrix are sequentially updated, are also considered for computing these
quantities. These techniques, together with some standard techniques using matrix inverses and generalized
inverses, are compared for accuracy, using some test problems from the literature.
[1]Grassman W.K., Taksar M.I., and Heyman D.P., Regenerative analysis and steady state distributions for
Markov chains, Oper. Res. 33, (1985), 1107–1116.
[2]Kohlas J. Numerical computation of mean first passage times and absorption probabilities in Markov and
semi-Markov models, Zeit fur Oper Res, 30, (1986), 197–207.
Numerical Continuation of Equilibria of an Atherosclerosis Model
Md Hamidul Islam
Griffith University, Brisbane, QLD, Australia
email: [email protected]
Coauthors: Peter R. Johnston
Atherosclerosis is a chronic inflammatory disease. Elevated concentration of low-density lipoprotein (LDL) and
their subsequent modification in arterial walls leads to the initiation and hence overall progression of this disease.
Endothelial dysfunction, resulting from modified lipoprotein in the arterial wall, permits accelerated transport
of monocytes into the arterial wall, where they differentiate into macrophages. Modified LDLs are then taken
up by the macrophages to form foam cells, which in turn initiate a series of intracellular events that may lead to
a chronic inflammatory process. This auto-amplified process leads to the formation of an atherosclerotic plaque.
We present a mathematical model of the early stages atherosclerosis obtained from a quasi-steady state approximation of a model proposed by Bulelzai and Dubbeldam (2012). We reduce the original model, consisting
of four ordinary differential equations, to a system of two ODEs. The remaining system describes the time
evolution of monocytes and macrophages. We perform a phase plane analysis on this reduced system corresponding to different parametric conditions to explore the role of monocytes/macrophages in the initiation of
an inflammatory process. Monocytes induce the oxidation of low-density lipoprotein (ox-LDL), and ox-LDL
in turn induces the migration of monocytes. Corresponding to different oxidation rates of LDL and migration
rates of monocyte, we obtain a range of initial monocyte concentrations which lead to different outcomes. Any
initial value chosen from this range leads to an inflammatory reaction, while the system remains healthy for
an initial state outside of this range. We also find that this range increases with the increasing uptake rate of
ox-LDL by the macrophage.
Influence of homeostasis on the long-time-limit behaviour of an autoimmune disease
Owen Jepps
Griffith University, Brisbane, QLD, Australia
email: [email protected]
Coauthors: Lindsay Nicholson and David Nicholson
We have recently developed ODE models for experimental autoimmune uveitis (EAU), a disease characterised
by T-cell-mediated inflammation of the retina and choroid. Uveitis is the second commonest cause of blindness
in the working population in the developed world. EAU serves not only as an important biological model for
uveitis in humans, but more generally in developing our understanding of autoimmunity and disease in immuneprivileged environments, where immune-cell species are compartmentalised inside and outside the relevant organ
(in our case the eye) during autoimmune disease. Interestingly, our mathematical models of EAU bear important
similarities with epidemiological models of mosquito-borne diseases such as malaria and dengue fever.
Despite their complexity, the long-time-limit behaviour of our models always leads to either a globally asymptotically stable (GAS) disease-free equilibrium (DFE), or an endemic equilibrium (EE) which is either GAS or
admits globally attracting limit cycles. In this talk I will discuss recent work in which we have used Lyapunov
functions to establish the global stability of the DFE and EE, under appropriate conditions on the parameters. I will also outline the crucial role played by the homeostasis terms, which describing the disease-free
cell-population dynamics, in determining the nature of the endemic dynamics.
Incorporating the effects of chemotherapeutic drugs into a multiphase model of cancer spheroid
Wang Jin
Queensland University of Technology, Brisbane, Australia
email: [email protected]
Multiphase models of cancer spheroid growth have been studied for about two decades, yet most studies focus
on models in one-dimensional Cartesian geometry. In this work we extend a spheroid model developed by
Breward and co-workers [1]. We obtain numerical solutions in a spherical geometry, and we classify three
different types of solutions: (i) travelling-wave-like, (ii) steady-state, and (iii) phase-separation solutions. We
further extend Breward’s model to include the effect of chemotherapy drugs. Using our numerical model we
study the responsiveness of the spheroid growth to three different classes of drugs, and we demonstrate how
different boundary conditions can be applied to mimic different drug treatment protocols.
1. Breward CJW, Byrne HM, Lewis CE (2002) The role of cell-cell interactions in a two-phase model for
avascular tumour growth. Journal of Mathematical Biology 45: 125–152.
A monomial transformation for evaluating two-dimensional nearly singular boundary element
Barbara Johnston
Griffith University, Nathan, Australia
email: [email protected]
When implementing the boundary element method, particular care must be taken with the evaluation of the
resulting singular and nearly-singular integrals. The latter category arises when the source point is close to, but
not on, the element of integration. This causes at sharp peak in the integrand because the source point is close
to the element, making accurate evaluation difficult. A sinh transformation method, which automatically takes
into account both the position of the projection of the source point onto the element and the distance b between
the source point and the element, has previously been introduced. This method has been shown to be superior
to existing methods in evaluating the 2D nearly singular potential and flux integrals that arise in the solution
of Laplace’s equation in three dimensions via the boundary element method. Here a similar, but alternative
method, based this time on a monomial transformation, is studied and compared with the sinh transformation
method. It is demonstrated that the new monomial method is particularly effective for very small values of b
(b ≤ 10−6 ), while remaining equally as easy to implement as the sinh transformation method.
Aggression Model for Wolbachia Flies
Peter Johnston
Griffith University, Nathan, Queensland, Australia
email: [email protected]
Coauthors: Jeremy Brownlie
Wolbachia is a mosquito bacteria used to control dengue fever and malaria. The effect of Wolbachia on the
mosquitoes is to shorten their lifespan and change their reproduction patterns. It is also thought that the
bacteria changes the way male and female insects interact with one another. Here we will develop a model for
male and female fruit flies (because they are used for laboratory experiments) both with and without Wolbachia
Consider a population of male and female flies, some of which are infected with Wolbachia. The basic breeding
model is as follows:
♂ × ♀ → 100% normal flies
♂w × ♀ → 0
♂w × ♀w →
♂ × ♀w →
95% Wolbachia infected flies
5% normal flies
95% Wolbachia infected flies
5% normal flies
where the subscript w indicates that the flies are infected with Wolbachia and × indicates a breeding event.
We will derive a simple system of four ordinary differential equations that takes into account the above breeding
rules and includes an “aggression” factor for mating relationships. For this system, we will examine the steady
states and study their stability.
How much information can be obtained from tracking the position of the leading edge in a scratch
Stuart Johnston
Queensland University of Technology, Queensland, Australia
email: [email protected]
Coauthors: Matthew Simpson and Sean McElwain
Collective cell behaviour is a key component of tissue repair and tumour spreading. Quantification of the
processes behind collective cell behaviour, namely the cell diffusivity, D, and the cell proliferation, λ, is critical
for the evaluation of putative treatments. We are therefore interested in developing mathematical techniques
that can be applied to experimental data to estimate D and λ. Scratch assays are a simple and inexpensive
method to observe collective cell behaviour. We describe a new method that combines scratch assay leading
edge data, discrete simulations and edge detection methods, which results in robust estimates of D and λ.
Steady Saturated-Unsaturated Water Flow in a Sloping Domain and its Application to Landslides.
Laura Karantgis
La Trobe University, Melbourne, VIC, Australia
email: [email protected]
Coauthors: Philip Broadbrige and Vincent Lemiale
Landslide events, often caused by heavy rainfall, can have a devastating impact on communities and industries.
Modelling these complex systems is valuable for predictive and preventative measures to assist in reducing the
impact of these events. As the soil water content affects slope stability we will need to model the distribution
of water in the soil and its effects on the soil strength parameters. In this talk we will construct a mathematical
water infiltration model to predict the behaviour of rainfall through a soil slope to assist in analysing the effects
of rainfall on the occurrence of landslides. Models for water infiltration flow through a porous medium have been
constructed using Darcy’s law and the Richards equation. In this talk we will use these equations to develop
a combined analytical and numerical approach to effectively create a two dimensional saturated-unsaturated
water infiltration model that can predict the water table and flow of water through soil for varying parameters
such as slope angle, length, rainfall rate and soil type.
Activating Lyapunov-based Feedback Design: Nonsmoothness and State Constraints
Christopher Kellett
University of Newcastle, Callaghan, NSW, Australia
email: [email protected]
In the 1990’s, significant progress was made in the use of Lyapunov-based techniques for design of feedback
stabilisers for systems described by ordinary differential equations. However, in the late 1990’s it was discovered
that for many important systems, these designs were not applicable. Feedback stabilisers applicable to a wider
class of systems, based on so-called nonsmooth control Lyapunov functions, were proposed in the early 2000’s,
though apparently never implemented. An additional drawback of both the original and newer Lyapunov-based
designs is that they do not account for state constraints. Herein, we describe the impediment to the original
Lyapunov-based designs. We also describe the newer designs and how they might be combined with ideas due
to Chetaev from the 1950’s to overcome the problem of dealing with state constraints.
Dynamics of systems with three timescales
Vivien Kirk
University of Auckland, Auckland, New Zealand
email: v.k[email protected]
Coauthors: Pingyu Nan, Yangyang Wang and Jonathan Rubin
Many physical systems have the property that some quantities evolve much faster than others. Dividing
timescales into two classes and applying techniques that exploit the timescale separation can yield significant insights about the dynamics of such systems. However, some dynamical phenomena cannot be captured
by a two timescale reduction and little is known about how to efficiently study systems with three or more
Motivated by applications in neural dynamics, this talk will discuss an ordinary differential equation model with
three timescales. We identify complex oscillations that appear to be intrinsically three timescale phenomena,
and use geometric singular perturbation theory to explain the mechanisms underlying these solutions.
Lewis Fry Richardson: pioneer of finite difference methods for partial differential equations
John Knight
University of Sydney, Sydney, Australia
email: [email protected]
Lewis Fry Richardson (1881-1953) was an English polymath who made important contributions to many fields
including numerical weather prediction, finite difference solution of partial differential equations, turbulent flow
and diffusion, fractals, and the causes of war. During World War I he invented the field of numerical weather
prediction, although his methods were not successfully applied until 1950, after the invention of fast digital
computers. Richardson’s first published papers in 1908 concerned the numerical solution of the free surface
problem of unconfined saturated soil water flow, arising in the design of drain spacing in peat. He favoured
finite difference rather than analytical solutions because he was attacking complicated real world problems which
needed numerical answers.
In his 1910 paper he mainly considered finite difference solutions for elliptic problems, but also developed finite
difference methods for the heat or diffusion equation, which he called ”marching methods.” He developed a three
time level explicit method, but needed to use an implicit two level method for the first time step. Unfortunately
he stopped the calculations too early to discover that his explicit method for the diffusion equation was unstable.
In 1947 Crank and Nicolson became famous by discovering that the Richardson explicit method was unstable,
and publishing the Crank Nicolson method which became very widely used. In fact what Crank and Nicolson
did was to use the same central difference method as Richardson for the first time step, and then use it for all
subsequent time steps. In 1910 Richardson could easily have done the same, but presumably preferred to use a
fully explicit method which involved much less calculation. So there is a strong case for calling the 1947 method
the Richardson-Crank-Nicolson method.
Frequency-domain Monte Carlo method for linear oscillatory gas flows
Daniel Ladiges
The University of Melbourne, Victoria, Australia
email: [email protected]
Coauthors: John Sader
Gas flows generated by resonating nanoscale devices inherently occur in the non-continuum, low Mach number
regime. Numerical simulation of such flows presents a tremendous challenge, which has motivated the development of several Monte Carlo methods for low Mach number flows. We present a frequency-domain Monte
Carlo method for oscillatory low Mach number gas flows, based on the linearised Boltzmann equation. This
circumvents the need for temporal simulations, providing direct access to both amplitude and phase information using a pseudo-steady algorithm. The proposed method is demonstrated with several examples, and good
agreement is found with both existing time-domain Monte Carlo simulations and accurate numerical solutions of
the Boltzmann-BGK equation. Further, we present a rigorous statistical method for analysing the convergence
of stochastic simulations. Using this approach, we show that simulations in the frequency-domain provide a
significant improvement in computational speed compared to existing time-domain Monte Carlo methods.
Exact derivation of a neural field model from a network of theta neurons
Carlo Laing
Massey University, Auckland, New Zealand
email: [email protected]
Neural field models are used to study macroscopic spatio-temporal patterns in the cortex. Their derivation from
networks of model neurons normally involves a number of assumptions, which may not be correct. We present
an exact derivation of a neural field model from an infinite network of theta neurons, the canonical form of a
Type I neuron.
Solving capacitated vehicle routing problems with time windows by goal programming approach
Dwi Lestari
Yogyakarta State University, Yogyakarta, Indonesia
Coauthors: Eminugroho Ratnasari and Atmini Dhoruri
Abstract. This paper presents how to build multiobjective linear programming model as solution of Capacitated
Vehicle Routing Problem with Time Windows (CVRPTW). We use a goal programming approach to solve the
model. We have discussed an objective function for two main goals: the first is to minimize the total number of
vehicles and the second is to minimize the travelling time of the used vehicles. The proposed model is applied
to a problem distribution of Liquefied Petroleum Gas (LPG). Computational results of the proposed model are
A Free Boundary Problem for Corporate Bond with Credit Rating Migration
Jin Liang
Tongji University, Shanghai, China
email: liang [email protected]
Coauthors: Bei Hu and Yuan Wu
In this work, a free boundary model for pricing a corporate bond with credit rating migration is proposed. This
is a new model for credit rating migration. The existence, uniqueness and regularity of the solution for the
model are obtained together with some interesting properties. Furthermore, numerical examples are presented.
Nanopterons in a granular chain
Christopher Lustri
University of Sydney, Sydney, Australia
email: [email protected]
We consider a simple model representing a chain of particles, each of which interacts only with its nearest
neighbours. This interaction is governed by an potential, which determines the behaviour of the particles when
they are disturbed. One particular model, known as the Toda chain, has been famously shown to admit soliton
In this study, we consider the behaviour of soliton-type solutions in a periodic Toda chain with particles of
alternating mass, where m1 and m2 represent the masses of the odd and even particles respectively. We are
particularly interested in the asymptotic behaviour when one set of particles is significantly heavier than the
other (ie. 0 < m1 /m2 1) . In this case, we find that the system no longer produces pure soliton solutions,
but instead the solutions take the form of nanopterons, or weakly nonlocal solitary waves. Specifically, we find
that the solitons produce an exponentially-small wavetrain in the far field of constant amplitude. We apply
exponential asymptotic methods to determine the behaviour of these far-field waves.
Pricing European options written on a hard to borrow stock
Guiyuan Ma
University of Wollongong, Wollongong, Australia
email: [email protected]
Coauthors: Songping Zhu
In this talk, we shall demonstrate how a restrictive trading environment with stocks being hard to borrow would
affect the price of an option with the introduction of a stochastic buy-in rate process. Following the framework
of Avellaneda and Lipkin’s (2009) innovative work, which proposed a model with dynamically coupled systems
between stock price and buy-in rate, we present two approaches to approximate the weight functions via the
Monte Carlo method. Furthermore, we propose a PDE approach to solve the European option problem with a
set of appropriate boundary conditions. Finally, we present some numerical results to show the quantitative price
drop of an European option written on hard-to-borrow stocks with dividend payments taken into consideration.
The wave equation is Toeplitz plus Hankel
Shev MacNamara
UNSW, NSW, Australia
email: [email protected]
We begin with the wave equation, which we show has Toeplitz parts and Hankel parts. The Hankel part comes
from the boundary, and we try to explain this. Examples with and without reflections are described.
Reference: “Functions of Difference Matrices Are Toeplitz Plus Hankel,” Gilbert Strang and Shev MacNamara,
SIAM Review (2014)
Scattering of acoustic plane waves by obstacles with corners: the effect of rounding.
Audrey Markowskei
Macquarie University, Sydney, NSW, Australia
email: [email protected]
Coauthors: Paul Smith
If an integral equation approach is employed as the basis of numerical studies of the scattering of plane waves
by an obstacle, a common technique for dealing with domains with corners is to round the corners. Using
an integral equation formulation designed for domains with smooth boundaries we examine the relationship
between the radius of curvature and the convergence of the solution as the radius tends to zero. We then
employ an integral equation formulation with a quadrature scheme using a graded mesh designed to achieve a
rapidly convergent solution for a domain with a corner exactly represented. A comparison of the two studies
allows us to examine the effect of rounding a corner, that is, the correlation between the radius of convergence
of the rounded corner and the true results from the domain with a corner. In all cases three different boundary
conditions are examined - Dirichlet, Neumann and an impedance condition.
The effect of surface wettability on droplet dynamics
Lisa Mayo
Queensland University of Technology, Brisbane, Australia
email: [email protected]
Coauthors: Scott McCue and Timothy Moroney
In agricultural spray applications, it is of great importance to maximise the retention of the spray formulation
by plant foliage. Since many plant species are resistant to wetting by water-based formulations, a surfactant
(surface active agent) is often added to the spray mixture in order to increase wettability by way of reducing
the interfacial surface tension and thus contact angle between the fluid and leaf surface. In this study, a thin
film model is used to simulate the dynamics of droplets in situations where the contact angle plays a major
role, such as spray applications. We simulate droplet motion on a virtual leaf surface and observe coalescence
behaviours which mimic experimental spray observations. We also consider how the wettability of a surface
influences the oval-corner-pearling transition of a sliding drop.
Depicting the outbreak and spread of algal blooms in New South Wales Lagoons using NOVA
Lynne McArthur
RMIT University, Melbourne, Australia
email: [email protected]
This project is inspired by the infrequent and random occurrence of algal blooms on Avoca Lagoon in central
New South Wales, Australia. The triggers for an algal event are poorly understood, as are the elements that
drive the spread. There was an outbreak in spring/summer 2012, when the lagoon was rapidly overcome with
the algae, which then dissipated by early January. The task here is to identify the conditions which trigger an
outbreak and then to estimate the extent and coverage of the bloom.stems.
In order to model the spread we have previously used MATLAB to program cellular automata models. This
report describes the use of NOVA, which allows a greater capacity to describe the dynamics of each cell and
thus more flexibility.
The project was designed around identifying the parameters which contribute to the outbreak of a bloom, and
those that drive the spread.
NOVA had proved to be particularly suited to this kind of modelling.
Exploring long-term drivers of pertussis resurgence and improved vaccine control strategies
James McCaw
University of Melbourne, Victoria, Australia
email: [email protected]
Coauthors: Patricia Campbell and Jodie McVernon
Mass vaccination against pertussis, introduced in many countries in the 1950s, dramatically reduced the impact
of this disease. However, several developed countries with longstanding immunisation programs, including
Australia, have experienced pertussis resurgence during the past decade.
We used mathematical models to identify the determinants of this increase, and define improved vaccine strategies to mitigate disease burden. We constructed a mathematical model of pertussis transmission explicitly
capturing the uncertainty in biological and immunological mechanisms thought to be important for transmission and protection. Multiple parameter combinations were simulated, and those which reproduced key features
of pertussis disease and infection in Australia were selected for use in predictive models. Simulated projections
compared the impact of alternative vaccination schedules on infection incidence.
Natural immunity lasting decades longer than vaccine immunity was needed to explain the initial control of
pertussis followed by late resurgence. The mean duration of natural immunity exceeded 50 years in almost 90%
of simulations matching observed epidemiologic patterns. Removal of a fourth (toddler) dose in Australia in
favour of an adolescent dose in 2003 was found to have contributed to resurgence, resulting in a 40% increase
in infections in the 18mth-¡4yr age group. Supplementing the existing five dose schedule with an 18mth dose
was the best future strategy, resulting in a 43% reduction in incidence in toddlers and 8% reduction in infant
incidence from 2014-2020.
Long-lasting natural immunity is important in driving long-term trends in pertussis cycles, which must be
considered when evaluating and designing vaccination strategies. Vaccine protection is comparatively shortlived, requiring multiple boosters over the first two decades of life for sustained direct and indirect protection.
This requirement is particularly marked in contexts where pertussis circulation is low, and opportunities for
natural boosting of immunity are limited.
Analytical expressions for infection path probabilities of an SIR model on small networks
Karen McCulloch
Massey University, Albany, New Zealand
email: [email protected]
A significant amount of effort has been directed at understanding how the structure of a contact network can
impact the spread of an infection through a population.
However, investigating how an infection spreads through large networks can be computationally expensive and is
seldom mathematically tractable. This research is focused on finding tractable results to aid our understanding
of how infections spread through networks. Given that there is one initial infectious individual (node) in a
network, how many other individuals are likely to become infected and which ones? Here, we use an SIR
(Susceptible-Infectious-Recovered) model for the spread of an infection to address questions like these for small
networks of different topological structure.
We also illustrate how we can use the results from small networks to analytically describe how the infection
spreads through a larger network. The key here is to correctly decompose the larger network into an appropriate
assemblage of small networks so that the results are exact.
Derivation of Fractional SIR Model
Anna McGann
UNSW, Sydney, Australia
email: [email protected]
Coauthors: Chris Angstmann, Bruce Henry and James Nichols
This talk will show the derivation for the governing equations that describe the evolution of an SIR model
for the spread of a disease in which the probability of recovering from the disease is a function of the time
since infection. The derivation is based on a stochastic process, a continuous time random walk, describing the
motion of individuals through SIR compartments. If the probability of recovering is power law distributed then
the governing equations involve fractional-order derivatives. It can be shown that the fractional order recovery
model is consistent with the general age-structured Kermack-McKendrick SIR model. I will also discuss steady
state solutions and numerical solutions of the governing equations.
Erupting Dusts
Mark McGuinness
Victoria University of Wellington, Wellington, New Zealand
email: [email protected]
Coauthors: Harpreet Singh
We present a new model for the initiation of high-speed eruptive two-phase dust flows in the laboratory. Shocktube experiments have been conducted on beds of solid particles in nitrogen under high pressure, which are
suddenly decompressed. Our model is successful in explaining the slab-like structures that are often observed
during initiation of bed movement, by considering the interaction between the compressible flow of gas through
the bed and the stress field in the particle bed, which ruptures when bed cohesion is overcome by the effective
stress in the bed generated by the gas flow. Our model includes the effects of overburden and wall friction,
and predicts that all layered configurations will rupture initially in this fashion, consistent with experimental
observation. We also find that the modelled dependence of layer size on particle size is a good match to
Wind power simulation using Correlated Innovation Matrix and Wavelet Multi-resolution Analysis approaches
Dougal McQueen
University of Canterbury, Canterbury, New Zealand
email: [email protected]
Coauthors: Alan Wood and Allan Miller
To meet carbon emissions targets, increased demand, and replace retiring plant it will be necessary to construct
new electricity generation plant in New Zealand. One of the least cost and carbon neutral methods of generating
electricity is wind power. The intermittent and variable nature of wind coupled with the passive reaction of
wind turbines ensures that wind power requires scheduled and spinning reserves. Reserve requirements can be
alleviated, to an extent, by distributing wind farms throughout the country, exploiting the diversity of wind.
However, spatial diversification may increase costs through reducing economies of scale in wind farm construction
and increasing transmission requirements. Transmission expansion has long lead times, and needs good models
of an uncertain future mix of generation size, type and location. There is insufficient measured wind power or
wind speed data to assess the trade-offs for envisaged wind development scenarios hence a model of wind power
is required. The model must be temporally and spatially congruent with respect to wind, demand, and other
generation types. In this paper specific models are developed applying wind speed time-series derived from a
Numerical Weather Prediction model, temporal interpolation methods, transformation to power using wind farm
power curves, and assumptions concerning electrical and operational efficiencies. The temporal interpolation,
or turbulence modeling, is achieved through two methods: a Correlated Innovation Matrix approach, and a
Wavelet Multi-Resolution Analysis approach. The models are used to simulate power time-series for seven wind
farms, and subsets of these used to assess a centralised scenario and a diversified scenario. Results are compared
with aggregate measured power time-series demonstrating the benefit of spatial diversification and illustrating
differences in the turbulence modeling approaches. Lastly progress toward a generalised model is discussed.
Spark - a new research tool for investigating novel bushfire spread concepts
Claire Miller
CSIRO Digital Productivity Flagship, Melbourne, Victoria, Australia
email: [email protected]
Coauthors: James Hilton, Andrew Sullivan and Mahesh Prakash
The improvement of faster than real-time bushfire spread models requires an increased understanding of underlying fire behaviour and spread mechanisms. Current simulation tools for operational use implement onedimensional rate of spread models extrapolated to two dimensions. This is done using methods such as the
assumption of fire shape or the adjustment of rates according to the angle between the front normal and the
wind direction. Environmental conditions are commonly predefined for computational efficiency and ease of
implementation. The next steps for improving these tools are to extend fire spread rate models beyond spread
in the direction of the wind and to investigate how the fire front affects its surroundings and, consequently,
Our bushfire spread prediction tool, Spark, has been developed with the functionality for use as a research
tool. Spark is based around a level set method which makes it both computationally efficient and adaptable
to complex fire behaviour and conditions. It can therefore effectively be used to investigate various phenomena
and increase understanding of bushfire spread. Elements of spread, such as rate equations and environmental
conditions, are all inputs with capabilities to provide dynamic calculations during simulation. Consequently,
new fire behaviour concepts can be easily added and investigated.
We provide examples of the use of Spark to study how different factors can impact the fire spread. The first
example is the inclusion of curvature of the fire front in the spread function. The second example is the
incorporation of variation in fuel and wind inputs.
Efficient and robust iterative solutions of the potential equation applied to modelling of electrochemical electrodes.
Tony Miller
Flinders University, Adelaide, Australia
email: [email protected]
The increasing use of battery technologies for remote energy storage and transport applications highlights the
importance of battery management systems. While traditionally such systems have used simple equivalent
circuits and empirical calibration factors, new approaches that make use of detailed electrochemical models are
being developed. These require solving an electrical conduction (potential) equation with non-linear current
sources terms at each step of a time-stepping approach. For this to be computationally feasible in a real
time battery management setting, the solution of this potential equation needs to be both efficient and, most
importantly, robust. This paper describes an iterative solution technique to do this. It can be thought of
as a kind of approximate Newton method with dynamic updating of the iteration parameters. The order of
convergence is one, however convergence can be proved under a wide range of conditions. A simple lumped
circuit approximation is used to start the iteration. Examples are given which show how the technique performs
in some extreme cases. The method is also applicable to other related electrochemical modelling problems.
How much does your social network reveal about you? Predictability and social information flow
Lewis Mitchell
University of Adelaide, Adelaide, SA, Australia
email: [email protected]
Coauthors: James Bagrow
The recent explosion in big data coming from online social networks has led to an increasing interest in bringing
quantitative methods to bear on questions in social science. Examples such as the study of emotional contagion
have led to substantial interest as well as controversy within this emerging field. In this talk we will discuss
one of the processes underlying emotional contagion, namely the flow of information between individuals in a
social network. Such an idea leads readily to the concept of predictability for an individual based upon their
friend network, allowing us to study how predictability relates to various social characteristics. By analysing
a massive data set of messages from Twitter using tools from information theory we present results relating
individual predictability and effective vocabulary size to numbers of friends and followers, as well as to cases
where one’s friend network is being monitored in order to predict that individual.
I’ve Got Fauxs in Different Area Codes.
John Mitry
The University of Sydney, Sydney, NSW, Australia
email: [email protected]
Folded singularities are commonly found in mathematical models of cellular activity. The canards associated
with these singularities distinguish between different solution behaviours. Thus canards can form physiologically
significant boundaries between solutions which represent varied cellular activity. We here present an analysis
of faux canards associated with folded saddle singularities. True canards pass from attracting manifolds to
repelling manifolds via folded singularities, while faux canards travel from attracting manifolds to repelling
manifolds also via folded singularities. There exists a 2-parameter family of faux canards in the vicinity of a
folded saddle singularity, while there exists only one true canard. We demonstrate and analyse the oscillatory
behaviour of faux canards about the primary faux canard, identifying a dependence on the ratio of the eigenvalues
associated with the saddle singularity. Additionally we demonstrate the existence of and characterise the set
of secondary faux canards, the number of which also depends on the eigenvalue ratio. Both of these form a
novel contribution to the study of faux canards and canards in general. If time permits we shall also describe
solutions associated with folded saddle singularities which follow one primary canard (true or faux) and then
switch to the other. These switching solutions can also possess oscillatory behaviour, which is itself also a novel
contribution. Given these results we observe that the folded saddle singularity, far from being straight forward,
is ludicrously complicated.
Enclosing solutions of the delay eigenvalue problem
Shinya Miyajima
Gifu University, Gifu-shi, Japan
email: [email protected]
Mathematical models consisting of delay-differential equations (DDEs), in the simplest form
= Ax(t) + Bx(t − τ ),
A, B ∈ Cn×n ,
τ ≥ 0,
occur naturally in a wide variety of fields related to applied mathematics, such as engineering, control theory,
biology, traffic modeling, neural networks, mechanics, and electronic circuits. One common approach for obtaining the solution of the DDEs is to solve the delay eigenvalue problem (DEP): find λ ∈ C and x ∈ Cn \ {0}
such that
(λI − A − Be−τ λ )x = 0,
where I is the n × n identity matrix. If λ and x satisfy this equality, then cxeλt is a solution of the DDEs, where
c ∈ C is an arbitrarily constant, which can be determined from initial conditions. From the above discussion,
the DEP is important.
Numerical methods for solving the DEP have been proposed by several researchers, e.g., Jarlebring, Sakurai,
and their colleagues. Since the DEP is the special case of nonlinear eigenvalue problems, numerical methods
for solving the nonlinear eigenvalue problems are also applicable. On the other hand, these numerical methods
rely on floating point arithmetic and thus cannot provide an exact solution of the DEP. Indeed, they usually
give only approximations to exact solutions.
In this talk, we consider enclosing the exact solutions of the DEP, specifically, computing intervals which contain
the solutions using floating point arithmetic. Such intervals are called “confidence intervals”, and give reliability
to the obtained approximations. While there are well-established algorithms for enclosing solutions of the other
problems, less attention has been paid to the DEP. When B = 0, the DEP reduces to the standard eigenvalue
problem. For the standard eigenvalue problem, effective and efficient methods for enclosing solutions have been
proposed in some literatures. On the other hand, these literatures do not mention how to extend these methods
to the DEP.
The purpose of this talk is to propose a method for enclosing the solutions of the DEP. This method computes
the interval containing the solution taking all the possible errors into account. In this method, the DEP is
reduced to a system of nonlinear equations, and the interval containing the solution of the nonlinear system is
computed based on the Newton operator and Brouwer fixed point theorem. This method moreover verifies that
the solution of the DEP contained in the interval is unique by checking the contraction property of the Newton
operator. We finally report numerical results to observe the properties of the proposed method.
Preconditioned finite volume methods on non-uniform grids for one-dimensional fractional diffusion equations
Tim Moroney
QUT, Brisbane, Australia
email: [email protected]
Coauthors: Alex Simmons and Qianqian Yang
Fractional diffusion equations are used to model anomalous diffusion processes where the particle scale behaviour
is not consistent with Brownian motion. Numerical methods for these equations must deal with fractional
derivatives, whose discretisations tend to produce dense coefficient matrices.
In this talk I present some recent work on a finite volume method for one-dimensional fractional diffusion
equations with Riemann-Liouville fractional derivatives on non-uniform grids. The method utilises a quadrature
scheme to discretise the fractional derivatives at control volume faces. The finite volume formulation ensures
mass conservation, while the non-uniform mesh allows for refinement in regions of interest.
For efficient numerical solution, matrix-free iterative solvers are used, thereby avoiding the need to form the dense
coefficient matrix. I discuss how an effective preconditioner can be constructed for this problem to accelerate
the convergence of the iterative solver. Furthermore, this preconditioner performs well on other, different-butrelated diffusion equations with fractional Laplacians, for which effective preconditioning has previously been
Epidemic detection and forecasting from surveillance data via Bayesian estimation
Robert Moss
Melbourne School of Population & Global Health, Melbourne, Australia
email: [email protected]
Coauthors: Peter Dawson and James McCaw
Meteorological forecasting methods combine mathematical models of the weather system with statistical inference methods (such as Bayesian estimation) to determine which model realisations are most likely to yield
observations consistent with those obtained from real-world surveillance.
The application of these methods to early detection and forecasting of disease epidemics (e.g., seasonal influenza)
is a recent innovation, and it remains unclear how extant surveillance systems and other rich data sources (e.g.,
social media) can be best used for such purposes. In addition, most of these studies have used non-mechanistic
statistical models and have therefore sacrificed the ability to develop significant insight into the mechanics of
the infection process.
We have begun using Bayesian estimation (via the particle filter) to couple mechanistic models of infection with
surveillance data from previous influenza seasons in order to evaluate the accuracy and precision of different
forecasting strategies during the early stages of an influenza epidemic. Preliminary results include quantification
of forecast accuracy as a function of forecasting date and surveillance characteristics (including observation
frequency and background noise levels). It is our intention to apply these forecasting methods to near-real-time
surveillance data during the 2015 Victorian influenza season and produce weekly forecasts, which we will then
be able to evaluate against the true epidemic.
A mechanism design approach to efficient dynamic market clearing
Ellen Muir
The University of Melbourne, Victoria, Australia
email: [email protected]
Coauthors: Peter Taylor and Simon Loertscher
In markets with buyers and sellers that arrive over time, we wish to determine the optimal market clearing policy
which maximises expected gains from trade. There is generally a cost associated with delaying trade while buyers
and sellers accumulate. However, there is also a loss of efficiency associated with clearing markets that contain
few buyers and sellers. We analyse several simple models which capture this tradeoff. Assuming buyers and
sellers arrive according to independent random processes, a variety of simplifying behavioural assumptions may
be introduced. Once a tractable model is fixed, all possible market clearing policies must be compared to
determine the optimal policy. To accomplish this, coupling techniques and dynamic programming methods can
be exploited. The results of this analysis have implications for simple dynamic matching markets, some classic
static mechanism design setups and lay the groundwork for a mechanism design analysis of dynamic centralised
Agent-based modelling of hepatitis B virus infection and clearance
John Murray
UNSW Australia, Sydney, NSW, Australia
email: [email protected]
Coauthors: Ashish Goyal
Hepatitis B virus (HBV) infection and replication occurs in liver hepatocytes. This comprises a dynamic process
within each infected cell describing the generation of new intracellular viral components, as well as infection
and the immune response throughout the liver. To properly describe this we constructed an agent-based model
where each agent represented an hepatocyte and where the state of each infected hepatocyte changed according
to the HBV infection cycle and the effects of various components of the immune system. We used the model to
test the relative roles of different mechanisms of the immune system in the clearance of acute HBV infection.
The time between infection and viremia clearance as well as the amount of liver turnover (HT), assessed against
literature estimates, were used as the two major criteria in determining reasonable outcomes. Modelling resulted
in 90% of cells containing between 1 and 17 HBV cccDNA (the template of HBV replication) copies and normally
distributed at the peak of infection, consistent with experimental findings. Variations in p36 levels, responsible
for determining export of virions or recirculation to amplify cccDNA numbers, had a much greater impact on
mean cccDNA levels/cell at peak viremia than virus infectivity and cccDNA half-life. Acute infection clearance
was possible with HT in the desired range of 0.7 to 1 provided a combined cytolytic and non-cytolytic immune
response occurred in conjunction with complete loss of intracellular viral components during cell proliferation.
This in silico model provided an excellent basis for investigation of HBV infection. No animals were harmed
during the course of these experiments.
The Lax pairs of discrete Painlev´
e equations arising from the integer lattice: (A2 + A1 )(1) case
Nobutaka Nakazono
The University of Sydney, Sydney, NSW, Australia
email: [email protected]
Coauthors: Nalini Joshi and Yang Shi
Construction of the Lax pairs of discrete Painlev´e equations from the Lax pairs of ABS equations are well
In this talk, I will show new method to obtain the Lax pairs of discrete Painlev´e equations by using the integer
lattice associated with ABS equations in detail by taking an example of q-Painlev´e equation with the affine
Weyl group symmetry of type (A2 + A1 )(1) .
This work supported by the Australian Research Council grant # DP130100967.
The effects of Wolbachia on dengue transmission dynamics
Meksianis Ndii
University of Newcastle, Newcastle, Australia
email: [email protected]
Coauthors: David Allingham, Roslyn Hickson and Kathryn Glass
The use of Wolbachia bacterium is a proposed new strategy against dengue. This can affect the dengue transmission dynamics, which is known to be seasonal. In the regions with strong variation in temperature and
rainfall, the dengue epidemic generally takes off only in certain time of the year. The time period when imported cases enter the population determines whether the outbreak occurs. This work investigates the effect
of Wolbachia on dengue transmission dynamics for different transmission rate, strength of seasonality. Our
results show that Wolbachia reduces the time-window in which outbreak can occur. The benefits of Wolbachia
depends on the transmission rate, with the bacteria most effective at moderate transmission rate. Also, as the
seasonality increases, the Wolbachia is less effective.
Biogas production in anaerobic bioreactors
Mark Nelson
University of Wollongong, Wollongong, New South Wales, Australia
email: [email protected]
Anaerobic digesters provide an efficient waste treatment method, reducing the organic loading of the waste
stream, whilst producing residues, both liquid and solid, that can be used as biofertilisers.
A further by-product of the digestion process is a methane rich biogas which can be converted, via combustion,
into electricity. It has been estimated that a substantial amount of the power requirements of an anaerobic
digester, perhaps all of the power requirements, could be obtained by optimising the production of the biogas,
which is a clean burning environmentally friendly fuel. The steady-state biogas production in an anaerobic
digester is investigated using an engineering model consisting of species equations in liquid and gas phases. The
model contains differential equations for eight substrates, five microbial species and four gases. There are six
rate expressions, thirty-three yield values and thirty-eight other parameter values (including initial conditions).
Some additional parameter values are required that are not specified in the paper.
Can we say anything useful about this model, or should we just whack the model equations into a continuation
Modelling reaction-diffusion systems with anomalous diffusion using a discrete time random walk,
with examples in modelling of HIV
James Nichols
UNSW, Sydney, Australia
email: [email protected]
Coauthors: Chris Angstmann, Bruce Henry, John Murray and Isaac Donnelly
In nature anomalous diffusion of particles often arises, for example in crowded environments or where trapping
occurs. Modelling of this diffusion system typically involves reaction-diffusion PDEs with fractional derivatives
(fPDEs). Solving these fPDEs, both analytically and numerically, is difficult. We proposed an numerical
method, the Discrete Time Random Walk, which approximates the fPDE. By virtue of being derived as a
physical stochastic process, conservation of mass is preserved and the method is stable. We present recent
developments, including demonstrations of multiple species reaction sub-diffusion systems, and applications of
these sorts of systems to early-infection dynamics in epithelial tissue of HIV.
Modeling wound closure in an epethelial cell sheet using the Cellular Potts Model
Adrian Noppe
University of Queensland, QLD, Australia
email: [email protected]
Coauthors: Zoltan Neufeld and Anthony Roberts
We use the Cellular Potts Model to simulate an epithelial cell layer and a microscopic wound, around one to five
cells, in two dimensions. Using an energy function to describe properties of the cells we find qualitative results
and insights into the wound closure process. The interaction between the contractile line tension due to the
actin ring around the perimeter of the cells and adhesion between the cells appears to play an important role
to determine whether a wound will open or close. This also suggests an active response, changing the balance
between contraction and adhesion, is required for the wound closure process to occur.
(Re)wiring network models to understand the economics of innovation.
Dion O’Neale
University of Auckland, Auckland, New Zealand
email: [email protected]
Here we analyze over 30 years of patent data from the European Patent Office to investigate patterns of regional
specialisation in different technical areas. We construct a bipartite network of over 4000 geographic regions and
over 600 areas of technology. We find that those regions that exhibit a revealed comparative advantage in a
larger number of technical areas (i.e. regions with high diversity) tend to, on average, have less ubiquitous
technologies in their patent portfolio than regions with lower technical diversity. Furthermore, we find that this
effect increases over time with low diversity regions holding patent portfolios whose contents become relatively
more ubiquitous. We use a number of null models to test a variety of potential hypotheses that might explain
the observed trend. The null models allow us to distinguish between intra-regional effects due to spillovers or
agglomeration, and effects due to exogenous factors such as regional populations and the relative abundance of
different technology codes. The null models involve re-wirings of the bipartite network according to different
heuristics intended to capture the above effects. The null models reveal that while the co-occurrence of codes
on patents (some inventions are commonly associated with multiple technologies) can account for the negative
correlation between mean ubiquity and diversity of regions, it leads to higher levels of mean ubiquity for
the region than are observed in the empirical data. This suggests that regions are exploiting spill-over and
agglomeration effects to specialize in low ubiquity combinations of technical capabilities.
Fast and stable spectral methods for PDEs
Sheehan Olver
The University of Sydney, Sydney, Australia
email: [email protected]
We describe a fast and stable approach to calculate the solution of general PDEs via global spectral methods,
based on formulation using Chebyshev and Ultraspherical polynomials. Many simple examples can be written as
generalized Sylvester equations solveable in O(n3 ) operations for n2 unknowns, which is a dramatic improvement
over the O(n6 ) operations required by collocation methods. Other examples can be written as a Kronecker
product of banded matrices, which also leads to an observed (but onproved) complexity of O(n3 ) operations.
This approach is used in the ApproxFun package for Julia to provide a black-box PDE solver.
Multiscale modelling of multicellular biological systems: mechanics, development and disease
James Osborne
University of Melbourne, Vic, Australia
email: [email protected]
When investigating the development and function of multicellular biological systems it is not enough to only
consider the behaviour of individual cells in isolation. For example when studying tissue development, how individual cells interact, both mechanically and biochemically, influences the resulting tissues form and function.
In this talk we present a multiscale modelling framework for simulating the development and function of multicellular biological systems (in particular tissues). Utilising the natural structural unit of the cell, the framework
consists of three main scales: the tissue level (macro-scale); the cell level (meso-scale); and the sub-cellular level
(micro-scale), with multiple interactions occurring between all scales. The cell level is central to the framework
and cells are modelled as discrete interacting entities using one of a number of possible modelling paradigms,
including lattice based models (cellular automata and cellular Potts) and off-lattice based models (cell centre
and vertex based representations). The sub-cellular level concerns numerous metabolic and biochemical processes represented by interaction networks rendered stochastically or into ODEs. The outputs from such systems
influence the behaviour of the cell level affecting properties such as adhesion and also influencing cell mitosis
and apoptosis. At the tissue level we consider factors or restraints that influence the cells, for example the
distribution of a nutrient or messenger molecule, which is represented by field equations, on a growing domain,
with individual cells functioning as sinks and/or sources. The modular approach taken within the framework
enables more realistic behaviour to be considered at each scale.
This framework is implemented within the Open Source Chaste library (Cancer Heart and Soft Tissue Environment, and has been used to model biochemical and biomechanical interactions
in various biological systems. In this talk we present the framework along with a demonstration of its applicability to modelling developmental processes.
Singularities in diffusion-driven flows
Michael Page
Monash University, Victoria, Australia
email: [email protected]
Independent studies by Wunsch and Phillips in 1970 showed that steady flow can be generated in a stable
density-stratified fluid simply due to the container having sloping insulated surface. Most of the analysis for
this type of problem has been undertaken within two-dimensional containers with uniformly sloping planar
surfaces in the small-R boundary-layer limit. However, external flows around objects in an unbounded fluid
can also exhibit unexpected features in that regime, a simple example of which is the sloping finite-length plate
considered by Woods (1991, J. Fluid Mech., 226, p625). Woods suggested a possible form of this flow but
more-recent numerical and experimental results show additional flow features near the ends of the plate.
In this talk, an asymptotic structure for Wood’s finite-length sloping plate problem is outlined in that limit.
Leading-order solutions are described, including in regions that extend horizontally from the ends of the plate,
which are present due to singularities at those points. This analytical structure is compared with both numerical
calculations at small R (or large Rayleigh number) and also published experimental results.
Dying in order: how crowding affects particle lifetimes
Catherine Penington
Queensland University of Technology, Brisbane, QLD, Australia
email: [email protected]
Coauthors: Matthew Simpson
Suppose we have several agents on a line. They move around randomly, but once they reach an end they
disappear permanently. How long will they survive? Without crowding effects, particles near the edges tend to
leave sooner than those at the centre, but there is a lot of variation. When crowding is included, and agents
cannot occupy the same position at the same time, both the mean time to disappear and its variance changes
dramatically. In this presentation, we use simulation and analysis to discuss the effects of crowding on agent
The apparent wake angle of a ship travelling in a fluid of finite depth
Ravindra Pethiyagoda
Queensland University of Technology, Brisbane, Queensland, Australia
email: [email protected]
Coauthors: Scott McCue and Timothy Moroney
For more than a century the characteristic wedge shape associated with the wake of a ship in infinitely deep
water was accepted to have a half angle of arcsin(1/3) ≈ 19.47◦ , known as Kelvin’s angle. Over the past one
or two years, however, this idea has been challenged by numerous papers documenting apparent wake angles
less than Kelvin’s angle, at least for sufficiently fast-moving “ships”. One key observation is that the apparent
angle we see in practice can be defined using the highest peaks of the wake. For finite depth flows there is
an analogue of Kelvin’s angle, here referred to as the caustic angle, that varies with the Froude number, F , a
nondimensional measure of speed. Using linear water wave theory, we calculate the apparent wake angles and
the caustic angles for a variety of ship speeds and fluid depths and shed light on some seemingly contradictory
results between these two measures.
What’s the catch?
Michael Plank
University of Canterbury, Christchurch, New Zealand
email: [email protected]
Coauthors: Jeppe Kolding and Richard Law
Regulations on minimum legal landing size are an almost universal tool in fisheries management worldwide. But
do we need them? To investigate this question, we combine an agent-based model of fisher’s decisions about
which fish sizes to target with a size-spectrum model of the population dynamics. The system settles to a Nash
equilibrium in which each individual fisher obtains the same expected catch. We compare the size distribution
of fish in the catch and the total yield with and without restrictions on the minimum size of fish that can be
caught. The results have implications for how fisheries can best be managed.
Stability of liquid films covered by a carpet of self-propelled surfactant particles
Andrey Pototsky
Swinburne University of Technology, Hawthorn, Victoria, Australia
email: [email protected]
Coauthors: Uwe Thiele and Holger Stark
We consider a carpet of self-propelled particles (swimmers) that move along the liquid-gas interface of a liquid
film on a solid substrate. The swimming direction of the swimmers changes in time due to rotational diffusion
and due to the fluid motion. We study the intricate influence of the swimmers on the stability of the film
surface and show that depending on the strength of in-surface rotational diffusion and the absolute value of
the in-surface velocity several instability modes can occur. In particular, the rotational diffusion can have a
stabilizing or destabilizing influence and may even suppress the instability entirely.
Numerical and analytical solutions of confined subdiffusion in three dimensions
Shanlin Qin
Queesland University of Technology, Brisbane, Australia
email: [email protected]
Coauthors: Fawang Liu and Ian Turner
Fractional order diffusion equations with a time fractional derivative of order (0 < α < 1) have been widely applied to model the anomalous subdiffusive system. In this paper, we consider a fractional subdiffusion equation
in three dimensions with the initial condition and reflecting boundaries. The fractional alternating direction
implicit scheme (FADS) is proposed to solve the fractional subdiffusion equation with different reflecting boundaries. Analytic solution is giving by using separation of variables method and showing a good agreement with
the numerical result. The stability and convergence of the method are proved. This initial-boundary problem
is applied to model practical subdiffusive problems like the motion of the real biomolecules inside cells.
The Evaluation of Faculty Employments Policies Using Markov Chain Model
Rahela Abdul Rahim
University Utara Malaysia, Kedah, Malaysia
Coauthors: Syafawati Saad, Haslinda Ibrahim, Farah Adibah Adnan and Sahubar Ali Nadhar
The approach to manpower policy in most Malaysian universities appears to be guided by the traditional
method of putting the right number of people in the right place at the right time or arranging for suitable
number of people to be allocated to various jobs usually in a hierarchical structure. The technique has been
practiced for years. This traditional method is deficit in the sense that it neither offers computational tools that
will enable managers to determine possible line of action to be taken nor provide tools to generate alternative
policies and strategies. The objective of this study was to design a planning model for projecting university
faculty employment under alternative policy suggested by government. The planning model was developed using
Markov chain technique. Two scenarios were considered in the study; scenario 1 was based on historical data
pattern between year 2005–2010 and scenario 2 was based on RMK 9 policies. Differences between actual and
projected numbers of faculty by status were tested using chi-square goodness of fit tests. The results showed
that there were no significance differences in the projected numbers of faculty by status for both scenarios. The
projection for diversity of faculty status based on the the two scenarios for year 2015 was also presented.
Effects of oblique magnetic field on mixed ferrofluid convection
Md. Habibur Rahman
Swinburne University of Technology, Melbourne, Victoria, Australia
email: [email protected]
Coauthors: Sergey A. Suslov
Magnetic fluid, also known as ferrofluid, is a stable colloidal suspension consisting of the carrier liquid and
magnetic nanoparticles. The behaviour of non-isothermal magnetic fluids strongly depends on external applied
magnetic field, which can be used to control flow and heat transfer in fluid in various technological applications.
Different mechanisms of convective instability manifest themselves in ferrofluid. In this talk we will present the
results of linear stability analysis for convection flow in a layer of ferrofuid bounded by two vertical differentially
heated plates placed in an external oblique magnetic field in the presence of gravity. The convective flows in
ferrofluid are driven by the ponderomotive force due to the magnetic field effects and by the buoyancy. A set
of characteristic ferrofluid parameters have been explored and thermomagnetic waves have been detected in a
ferrofluid flow. The influence of the external magnetic field inclination angle on the flow structure is investigated.
The Probability of Bushfire Ignition
Nicholas Read
The University of Melbourne, VIC, Australia
email: [email protected]
Bushfire is a significant and increasing threat to Australia. It is an old threat and the scientific literature on
forecasting bushfire is large although perhaps not as diverse as it could be. This talk will outline the practical
problem, discuss the currently popular logistic regression models before proposing some point process models
for lightning fire ignition.
Hybrid Markov chain models for disease dynamics.
Nicolas Rebuli
The University of Adelaide, Adelaide, Australia
email: [email protected]
Coauthors: Nigel Bean and Joshua Ross
Continuous-time Markov chains (CTMCs) continue to increase in popularity for modelling disease dynamics.
They owe their popularity to often finding an appropriate balance between computational feasibility and sufficient realism. However, this balance is lost as the size of the population being modelled increases, due to
a ‘curse of dimensionality’. In this talk I consider the susceptible–infectious–recovered (SIR) CTMC epidemic
model and present two novel methods for overcoming this dimensionality problem. The so called SIR hybrid
models approximate the SIR CTMC on a subset of its state space using either a deterministic, or a diffusion,
approximation. I assess the accuracy of the hybrid models by comparing their final epidemic size and epidemic
duration distributions to those of the SIR CTMC.
Multiphase modelling of biological gel mechanics
James Reoch
University of Adelaide, SA, Australia
email: [email protected]
Cells are often grown within collagen gels in vitro for applications in tissue engineering. Since the behaviour
of cells is regulated by their mechanical environment, we aim to gain more insight into the mechanics of these
gels using mathematical modelling. In this talk, I will outline the modelling approaches being used to study the
mechanical interactions between the cells and the gel. A novel aspect of the problem is the inclusion of chemical
effects such as osmosis, which, together with the forces exerted by the cells, drive gel contraction and swelling.
I will present our current multiphase model, discussing its steady state behaviour and numerical simulations of
its time evolution.
Folded Saddle-Node Bifurcations
Kerry-Lyn Roberts
University of Sydney, NSW, Australia
email: [email protected]
Coauthors: Martin Wechselberger and Jonathan Rubin
Folded saddle-node (FSN) bifurcations occur generically in one parameter families of singularly perturbed
systems with at least two slow variables. Recently we identified a novel FSN bifurcation (FSN III) in a coupled
neural model. In this talk we analyse a canonical model of the FSN III bifurcation. We combine techniques
from geometric singular perturbation theory (the blow-up technique) and dynamic bifurcation theory (complex
time path analysis) to understand the local dynamics and show the existence of canards.
Understanding risk through virtual sensing: an application to the agricultural industry.
Melanie Roberts
IBM Research - Australia, Melbourne, Victoria, Australia
email: [email protected]
Crop yield is impacted by the weather. Accurate risk modelling of the yield across several geographies remains a
challenge due to sparsity and access to yield and/or fine resolution weather data. The sparsity of fine resolution
of weather data is addressed through dynamical downscaling and post-processing methods. The impact of the
downscaled weather data on crop yield is studied using historical yield data. The weather data then forms the
basis for developing an accurate crop yield risk model.
Exponential growth and the final size of an epidemic
Mick Roberts
Massey University, Auckland, New Zealand
The value of the basic reproduction number, R0 , may be estimated when the incidence of infection is growing
exponentially in the early stages of an epidemic. For the Kermack-McKendrick model the final size of the
epidemic - the proportion of the population that would be infected if no interventions were made - depends
only on R0 and the initial proportion susceptible. This well-known result will be generalised to the situation
where R0 has an uncertain estimate, specified as a probability distribution. A stochastic SIR model will then
be described, where the contact rate fluctuates randomly, and the initial growth rate and final size determined.
Epidemics in a heterogeneous population due to an infection spread by a vector or environmental contamination
may be modelled with so-called separable mixing. Expressions for R0 and the final size will be obtained, and
compared with those for an epidemic on a network.
High-order evolution PDEs model nonlinear dispersive waves over large scales
Tony Roberts
University of Adelaide, South Australia, Australia
email: [email protected]
Many practical approximations in science and engineering involve wave propagation over a relatively long
physical domain. In this scenario we typically expect the waves to have structures that vary slowly in the long
dimension. Extant approximation methodologies are typically self-consistency arguments. The proposed new
approach is to analyse the dynamics based at each cross-section in a rigorous Taylor polynomial. Slow manifold
theory supports the local modelling of wave modulation with coupling to neighbouring locales treated as a
non-autonomous forcing. The union over all cross-sections then provides powerful new support for the existence
and relevance of a slow manifold, wave modulation. Our resolution of the coupling between neighbouring locales
leads to novel quantitative estimates of the error. The approach developed here may be used to quantify the
accuracy of known approximations, to extend such approximations to mixed order modelling, and to open
previously intractable modelling issues to new tools and insights.
A nonlinear least squares approach to time of death estimation via body cooling
Marianito Rodrigo
University of Wollongong, Wollongong, NSW, Australia
email: marianito [email protected]
The problem of time of death estimation by body cooling is revisited by proposing a nonlinear least squares
approach that takes as input a series of temperature readings only. Using a reformulation of the Marshall-Hoare
double exponential formula and a technique for reducing the dimension of the state space, an error function
that depends on the two cooling rates is constructed, with the aim of minimising this function. Then an explicit
formula for the time of death is given. Results of numerical simulations using both theoretical and experimental
data are presented, both yielding reasonable estimates.
The proposed procedure does not require knowledge of the temperature at death nor the body mass. In fact,
the method allows the estimation of the temperature at death once the cooling rates and the time of death have
been calculated. The procedure requires at least three temperature readings, although more measured readings
could improve the estimates. With the aid of computerised recording and thermocouple detectors, temperature
readings spaced 10-15 minutes apart, for example, can be taken.
Solutions of the discrete Painlev´
e equation q-P (A∗1 ) which are meromorphic at the origin or infinity.
Pieter Roffelsen
University of Sydney, Sydney, Australia
email: [email protected]
In a series of papers Kaneko and Ohyama classified all the meromorphic solutions of the continuous Painlev´e
equations around fixed singularities of Briot-Bouquet type. Using a q-discrete analogue of the celebrated BriotBouquet Theorem we classify the solutions of the q-P (A∗1 ) equation which are meromorphic at the origin or
infinity. For these special Painlev transcendents, we construct global solutions of the Lax pair of q-P (A∗1 ) around
z = 0 and z = ∞ and consider the corresponding connection problem.
Condition numbers in conic feasibility problems
Vera Roshchina
University of Melbourne, Melbourne, Australia
email: [email protected]
Coauthors: Javier Pena
Condition numbers in conic optimisation quantify the difficulty in solving a problem’s instance. There are
different condition numbers which capture distinct geometric properties of the problem; some are better suited
for the characterisation of complexity of numerical methods, others serve better for the analysis of the problem’s
geometric properties. Of particular interest are the ill-posed problems, and the issues of preconditioning,
particularly in the linear programming setting.
The talk is based on collaborative work with Prof. Javier Pena (Carnegie-Mellon University)
Computation of epidemic final size distributions
Joshua Ross
The University of Adelaide, Adelaide, South Australia, Australia
email: [email protected]
Coauthors: Andrew Black
An important statistic associated with the outbreak of an infectious disease is the total number of individuals
that contract the disease. Such final size data is highly informative to estimate the transmissibility of a disease. In these situations the accurate and efficient computation of the probability of each possible final size is
paramount. A new method for the computation of the final size distribution for Markovian epidemic models
will be presented. For the case of the S-I-R (susceptible-infectious-recovered) model, this is the most efficient
algorithm produced. The method is also physically transparent, and hence allows relatively easy extension to a
range of more complex models, such as those with a phase-type infectious period and/or with waning immunity.
Complex Network Transformations of Time Series: the Ordinal Partitions Method
Konstantinos Sakellariou
University of Western Australia, Perth, WA, Australia
Recently several methods which utilise complex network theory as a means of analysing time series have been
developed. Nodes may represent regions in phase space, dynamical states or even time series points. Network
connectivity is defined in such a way so as to capture specific information about the dynamical systems generating
the time series. We explore the so-called ’ordinal partitions’ network transform, a transformation technique
where nodes encode discrete dynamical states and network connectivity is defined by temporal succession.
Consequently, dynamical information and modes of transition from state to state are the focus here - in contrast
to the majority of the existing network transforms which concentrate on topological aspects. By applying this
technique to data generated by numerical simulation of model chaotic dynamical systems (e.g. Lorenz system,
Ikeda map), we perform a parameter investigation. We determine the ’interesting’ parameter regimes in terms
of applicability and test the robustness of the method in the presence of noise. We then analyse the resulting
networks and identify how their local and global statistical properties reflect the underlying dynamics governing
the original time series. In particular, we examine the relation between network properties and important
dynamical notions, such as unstable periodic orbits or recurrence of states on a chaotic attractor.
Fractional-in-space partial differential equations on finite intervals, boundary conditions, and
associated stochastic processes
Harish Sankaranarayanan
University of Otago, Dunedin, New Zealand
email: [email protected]
Coauthors: Boris Baeumer and Mih´
aly Kov´
We present Gr¨
unwald approximations for fractional derivative operators on finite intervals, whose domains
encode various boundary conditions. The well-posedness of the Cauchy problem associated with fractional
derivative operators on C0 (Ω), L1 (Ω), Ω ⊂ R is established. The stochastic processes associated with fractional derivative operators are identified as limits of the processes associated with the respective Gr¨
The probability of extreme rain on your parade given the El Ni˜
no Southern Oscillation
Kate Saunders
University of Melbourne, Melbourne, Australia
email: [email protected]
Courtesy of agricultural stakeholders, mean rainfall processes in Australia are fairly well understood; conversely
the drivers and processes behind extreme rainfall still pose a significant question for researchers. We use extreme
value theory to quantify how the large scale climate driver of the El Ni˜
no Southern Oscillation (ENSO) alters the
distribution of extreme daily rainfall events in Australia. We do this by fitting a generalized Pareto distribution
to the high-quality sites in the Bureau of Meteorology’s climate change network. The observational record for
these sites spans approximately 100 years allowing us to make more statistically significant conclusions about the
effect of ENSO on the distributions parameters than studies that have come before. For sites where significance
is not detected, we are still faced with the question of whether given the size of our observational set, should
we have reasonably been able to detect significance. We also aim to address this.
Tractable Quadrature in Infinite Dimensions and Applications in Uncertainty Quantification
Robert Scheichl
University of Bath, Bath, UK
email: [email protected]
Coauthors: Frances Kuo, Christoph Schwab, Ian Sloan and Elisabeth Ullmann
The coefficients in mathematical models describing physical processes are often impossible to determine fully
or accurately, and are hence subject to uncertainty. It is of great importance to quantify the uncertainty in
the model outputs based on the (uncertain) information that is available on the model inputs. This invariably
leads to very high dimensional quadrature problems associated with the computation of statistics of quantities
of interest, such as the time it takes a pollutant plume in an uncertain subsurface flow problem to reach the
boundary of a safety region or the buckling load of an airplane wing.
Higher order methods, such as stochastic Galerkin or polynomial chaos methods, suffer from the curse of dimensionality and when the physical models themselves are complex and computationally costly, they become
prohibitively expensive in higher dimensions. Instead, some of the most promising approaches to quantify
uncertainties in continuum models are based on Monte Carlo sampling and the “multigrid philosophy”. Multilevel Monte Carlo (MLMC) Methods have been introduced recently and successfully applied to many model
problems, producing significant gains.
In this talk I want to recall the classical MLMC method and then show how the gains can be (significantly)
improved further by using quasi-Monte Carlo (QMC) sampling rules. More importantly the dimension independence and the improved gains can be justified rigorously for an important model problem in subsurface flow.
To achieve uniform bounds, independent of the dimension, it is necessary to work in infinite dimensions and to
study quadrature in sequence spaces. I will present the elements of this new theory for the case of lognormal
random coefficients in a diffusion problem and support the theory with numerical experiments.
A geometric construction of shock waves in a tumour growth model, incorporating the Allee
Lotte Sewalt
Leiden University, Leiden, The Netherlands
email: [email protected]
Coauthors: Kristen Harley, Peter van Heijster and Sanjeeva Balasuriya
We discuss the influence of growth thresholds on the existence of travelling shock wave solutions in a reactionadvection-diffusion model describing the invasion of malignant tumour cells. Using geometric singular perturbation theory (GSPT) and canard theory, the existence of travelling shock waves as a solution to this PDE
system is proved. In earlier work, the spread of cancer cells was modelled as logistic growth. However, recent
studies have shown that such processes are often characterized by growth thresholds, a phenomena known in
ecology as the Allee effect and one that cannot be described by a logistic term. We show how incorporating
this effect changes our existence results.
An Individual-based model approach to analyse the spatio-temporal dynamics of Influenza in
Shrupa Shah
The University of Melbourne, Melbourne, Australia
email: [email protected]
Influenza is a major public health concern as it causes significant morbidity in the population at large and
mortality in the very young, elderly and in persons with chronic illnesses. The 1918–1919 Spanish flu and 2003
SARS (Severe Acute Respiratory Syndrome) pandemics are stark reminders of the potential consequences of
infectious diseases. Although the SARS epidemic was not the world-wide pandemic that scientists feared, it still
managed to spread to nearly every continent on Earth. This clearly points out how crucial it is to understand
how, when and why epidemics spread across the landscape so that effective planning, preparation and control
measures can be in place before a disaster occurs.
Geographic models can help us understand the spatial spread from the epicentre and the rate at which the
disease diffuses from the epicentre. This will then inform control strategies like contact tracing and quarantine
during the initial phases of the outbreak and ring vaccination or some other control strategy at later phases of the
epidemic. In the light of this, I will briefly review some of the mathematical, computational and network models
from the literature which implicitly or explicitly consider space and the assumptions these models make. I will
also review the applications of some spatio-temporal models successfully implemented. And finally conclude
with, how these applications motivate the early framework for my project which is also strongly informed by a
field study conducted in Melbourne where data has been collected at the individual level of granularity. With
the proposed framework I hope to investigate how seasonal Influenza spreads in Melbourne.
Modelling the intrinsic dynamics of bushfire propagation using plane curvature flow
Jason Sharples
UNSW, Canberra, ACT, Australia
email: [email protected]
Coauthors: James Hilton
Bushfires are inherently dynamic phenomena that consistently pose threats to society and the environment.
Despite their dynamic nature, current operational approaches to predicting the spread of bushfires are based on
first-order propagation models, which assume that fires spread at a quasi-steady state defined by the relevant
environmental variables. In this work we report on initial investigations into the use of a second-order propagation model, which incorporates a functional of the fire line curvature to emulate intrinsic fire line dynamics.
The model is implemented in the form of a curvature flow via a level set method. Application of the work to
modelling fire coalescence will also be discussed.
Modelling Tumour Treatment using the Single Species Gompertz Population Model
John Shepherd
RMIT, Melbourne, Victoria, Australia
email: [email protected]
Coauthors: Stuart E Roberts
In 1825, Benjamin Gompertz proposed his well-known equation to model constrained human population growth.
In the 1960s, A K Laird used this Gompertz equation to model the growth of tumours as growing cell populations
in a confined space. This approach has been used and extended by many investigators.
A logical consequence of this is that the treatment of tumour growth by chemical or radiative means could be
modelled by a harvested Gompertz equation with density dependent harvesting.
A complication occurs if the parameters defining the harvesting model are no longer constants, but vary with
time, as might occur in a varying environment. Then, for completely arbitrary time variation, exact solution of
the harvested equation is rarely possible, and we must resort to numerical solutions, which have the disadvantage
of requiring explicit parameter values and are of limited use in studying general trends. However, when the
model parameters are slowly varying functions of time, multitiming techniques may be used to obtain explicit
and useful approximations for the variation of the tumour population.
In this talk, we use these techniques to analyse the harvested Gompertz model and use the approximations
obtained to make useful predictions about the evolving population and related quantities of interest.
Symmetry and combinatorics of Coxeter groups and discrete integrable systems
Yang Shi
The University of Sydney, Sydney, NSW, Australia
email: [email protected]
Coauthors: Nalini Joshi, Nobutaka Nakazono
From the geometric and combinatorial descriptions of the Coxeter groups we construct various discrete integrable
systems and show that the relationships between these different systems can be naturally explained using such
Chemotactic adhesion in bacterial flocs in shear flow: a multi-scale model
Sarthok Sircar
University of Adelaide, Adelaide, SA, Australia
email: [email protected]
In this talk, I present a model for the attachment/detachment dynamics of bacterial aggregates in a fluid
subject to a homogeneous planar shear-flow. To understand the adhesion-fragmentation dynamics of these
flocs, the aggregates are modeled as ligand-covered rigid spheres. The binding ligands on the surface of the flocs
experience attractive and repulsive surface forces in an ionic medium and exhibit finite resistance to rotation (via
bond tilting). For certain range of material and fluid parameters, the results predict a nonlinear or hysteretic
relationship between the binding/unbinding of the floc surface and the net floc velocity (translational plus
rotational velocity). I show that the surface adhesion is promoted by increased fluid flow until a critical value,
beyond which the bonds starts to yield. Moreover, adhesion is promoted in a medium with high ionic strength,
or flocs with small size or lower binder stiffness. The numerical simulations of floc-aggregate number density
studies support these findings.
Do pioneer cells exist?
Matthew Simpson
Queensland University of Technology, Brisbane, Australia
email: [email protected]
Most mathematical models of collective cell spreading make the standard assumption that the cell diffusivity
and cell proliferation rate are constants that do not vary across the cell population. Here we present a combined
experimental and mathematical modeling study which aims to investigate how differences in the cell diffusivity
and cell proliferation rate amongst a population of cells can impact the collective behavior of the population.
We present data from a three–dimensional transwell migration assay which suggests that the cell diffusivity of
some groups of cells within the population can be as much as three times higher than the cell diffusivity of
other groups of cells within the population. Using this information, we explore the consequences of explicitly
representing this variability in a mathematical model of a scratch assay where we treat the total population of
cells as two, possibly distinct, subpopulations. Our results show that when we make the standard assumption
that all cells within the population behave identically we observe the formation of moving fronts of cells where
both subpopulations are well-mixed and indistinguishable. In contrast, when we consider the same system
where the two subpopulations are distinct, we observe a very different outcome where the spreading population
becomes spatially organized with the more motile subpopulation dominating at the leading edge while the less
motile subpopulation is practically absent from the leading edge. These modeling predictions are consistent
with previous experimental observations and suggest that standard mathematical approaches, wherewe treat
the cell diffusivity and cell proliferation rate as constants, might not be appropriate.
This is joint work with Emeritus Professor Sean McElwain and Ms Parvathi Haridas.
Modelling Overwash on Ice Floes by Water Waves
David Skene
The University of Adelaide, Adelaide, Australia
email: [email protected]
Ocean waves have a significant impact on the vast regions sea ice covering the surfaces of the high-latitude
oceans. Contemporary mathematical models of wave-ice interactions are based on linear theory: using potential
theory for the water and thin-elastic-plate theoryfor the ice floes (discrete chunks of sea ice). In reality, highly
non-linear effects occurin wave-ice interactions.
In particular, a phenomenon known as overwash occurs. Overwash refers to thin streams of water being forced
over the top of floes as their edges dip in and out of the surrounding water waves.
I will present a mathematical model of overwash. The model uses linear theory for the motion of the floe and
the water surrounding the overwash region. The surrounding water drives the overwash. The overwashed water
itself is modeled using the nonlinear shallow-water equations. Model results arevalidated usingresults of an
experimental model.
The ANOVA decomposition of a non-smooth function of an infinite number of variables
Ian Sloan
UNSW, Sydney, Australia
email: [email protected]
In this joint work with Frances Kuo (UNSW) and Michael Griebel (Bonn) we extend our earlier work motivated
by path-dependent option pricing problems, in which we tried to understand how it is that sparse grid and
QMC methods can be applied successfully to option pricing problems, even though the integrands do not live
in any mixed derivative smoothness class. That difficulty derives from the “max function” in the integrand,
describing the fact that options are considered worthless if the payoff falls below the strike price.
In a previous paper (Math. Comp. 82, 383–400, 2013) we showed that if the expected value is expressed as an
integral over Rd then the classical ANOVA decomposition of the integrand for an arithmetic Asian option can
have every term smooth except for the very highest term. That highest ANOVA term has many discontinuities
in first partial derivatives, but in most cases is expected to be pointwise very small.
In the present work we consider the ANOVA decomposition of the corresponding continuous problem in the
Brownian bridge (or Levy-Ciesielski) formulation, and show that in this case every term in the (infinite)
ANOVA decomposition is smooth. With this result we are preparing for an error analysis of the cubature
problem for option pricing problem, in which the discrete-time problem is approximated by the continuous
problem, and the error analysis then applied to the truncated infinite ANOVA expansion, in which every term
is smooth.
The (un)importance of the temperature gradient in fibre drawing.
Yvonne Stokes
The University of Adelaide, Adelaide, SA, Australia
email: [email protected]
An optical fibre is fabricated by feeding a preform into a heated neck-down region and pulling it at a higher
speed by winding onto a spool some distance downstream beyond the neck-down region. The existence of a
strong temperature gradient (50-100 ◦ C/cm) along the length of the neck-down region (typically 2-4 cm) is
essential to this process and much work has been done by others on the difficult task of modelling to determine
the temperature, and hence the viscosity, profile. I will, however, show that obtaining a desired fibre geometry
essentially depends only on the harmonic mean of the temperature over the neck-down length and, indeed, that
control of the fibre tension circumvents the need to know anything about the temperature profile.
Non-linear thermomagnetic instabilities in a vertical layer of a ferromagnetic fluid
Sergey Suslov
Swinburne University of Technology, Hawthorn, Victoria, Australia
email: [email protected]
Coauthors: Pinkee Dey
Nonlinear instabilities have been studied to reveal the exact mechanism leading to the appearance of various
convection patterns arising in a differentially heated vertical layer of non-conducting ferromagnetic nanofluid
placed in an external uniform magnetic field normal to the layer. Depending on the governing parameters,
developing instability patterns consist of vertical stationary magneto-convective rolls and vertically counterpropagating thermo-gravitational or oblique thermo-magnetic waves (Suslov, Phys. Fluids 20, pp. 1–18, 2008).
Weakly nonlinear analysis based on combined amplitude and multiple time scale expansions is applied to
investigate those interacting patterns. Squire’s transformation is extended to include nonlinear terms to reduce
the full three dimensional problem to an equivalent two dimensional problem and to keep the computational cost
down. The character of bifurcations is analysed in detail to provide parametric guidance for future experiments.
Symmetric 4-body motions
Winston Sweatman
Massey University, Auckland, New Zealand
email: [email protected]
The gravitational N-body problem has a rich and varied dynamics. We consider 4-body systems which are
further simplified by having a symmetric arrangement. There are families of orbits analogous to earlier families
of orbits found in the 3-body problem.
Random coefficient autoregressive model and Maximum quasi likelihood estimation
Laleh Tafakori
University of Melbourne, Melbourne,victoria, Australia
email: [email protected]
We consider the specific kind of random coefficient autoregressive model and their statistical properties. Further,
Maximum quasi likelihood estimation (MQE) which has many of the desirable properties of MLE, without
requiring the existence of an objective function too be maximized, is derived. Therefore, the difficulties arising
from the discontinuous likelihood function of the mentioned model can be avoided by using MQE.
Reflection methods for Euclidean distance matrix reconstruction
Matthew Tam
University of Newcastle, Newcastle, NSW, Australia
email: [email protected]
Coauthors: Francisco Arag´
on Artacho and Jonathan Borwein
The Douglas-Rachford reflection method is a general purpose algorithm useful for solving the feasibility problem
of finding a point in the intersection of finitely many sets. Despite a lack of theoretical justification, the method
has recently been experimentally observed to successfully solve a variety of difficult non-convex optimisation
and inverse problems including Sudoku puzzles, finding Hadamard matrices, and numerous image reconstruction
problems. In this talk I will focus on application of the Douglas-Rachford method to the (non-convex) problem
of reconstructing a Euclidean distance matrix from a priori knowledge, and a small subset of its entries. The
framework is then applied to the problem of protein conformation determination.
On solutions of a functional PDE for cell growth and division
Steve Taylor
University of Auckland, Auckland, New Zealand
email: s[email protected]
Coauthors: Susan Yang
We study the existence of solutions of a functional PDE model for size-structured cell growth and division,
introduced by Graeme Wake et al.
In this model, the density of cells relative to cell size x at time t is denoted n(x, t). A cell of size x is assumed
to divide into two new cells of size αx and βx . Taking into account growth rate g, splitting rate b and death rate
µ results in the model
n(x, t) +
(g(x)n(x, t)) = −(b + µ)n(x, t) + bαn(αx, t) + bβn(βx, t),
n(0, t) = 0, n(x, 0) = n0 (x), lim n(x, t) = 0.
A natural space for solutions is L1 because the total number of cells should be finite;
Z ∞
n(x, t)dx < ∞.
In this talk, we give a simple proof of existence of solutions in Lp for p ≥ 1.
How old is this bird?
Peter Taylor
University of Melbourne, Victoria, Australia
email: [email protected]
Coauthors: Sophie Hautphenne
Motivated by studies of a population of black robins (Petroica traversi ) in the Chatham Islands, we consider
the situation where an individual’s lifetime is modelled by a finite-state continuous-time Markov chain with
one absorbing state. Under this model, the time of death follows a phase-type distribution. We then attempt
to provide an answer to the simple question “What is the age distribution of the individual, given its current
phase”? There are a number of ways to think about this question, which we shall discuss. In particular, we
show that the answer depends on the observation scheme under consideration.
Optimal vaccine allocation for structured populations
Mingmei Teo
University of Adelaide, Adelaide, SA, Australia
email: [email protected]
Coauthors: Nigel Bean and Joshua Ross
Vaccination is the most effective method for preventing the spread of an infectious disease. In many scenarios,
vaccines may be in short supply or may be very expensive, and hence determining their optimal deployment will
be of great interest. Examples include in the early stages of vaccine production following the identification of a
suitable vaccine during an outbreak, as anticipated to be the case for Ebola in West Africa; or, in the control
of livestock diseases, where maintaining disease-free premises at minimal cost is desired. We consider dynamic
programming approaches to determine the optimal allocation of vaccines across a small number of interacting
populations/households in order to minimise the mean final epidemic size.
Towards an extended Navier-Stokes hydrodynamics at the nanoscale
Billy Todd
Swinburne University of Technology, Hawthorn, Victoria, Australia
email: [email protected]
In this presentation, both theoretical and simulation studies are highlighted that clearly demonstrate the importance of several non-classical phenomena fundamental to the extension of Navier-Stokes hydrodynamics for
highly confinded fluids. These are: (1) the prevalence of slip, (2) the strong coupling of molecular spin to linear
translational momentum, and (3) the non-locality of viscous transport at the nanoscale. In the first of these,
we utilize a newly developed equilibrium based model1 to accurately predict the slip velocity and slip lengths of
systems such as water or methane flowing in graphene nanochannels and carbon nanotubes2,3 . We demonstrate
that traditional molecular dynamics simulations of such systems are far less efficient and accurate than the
easily implemented model we propose. Next, we show that ignoring the coupling of spin angular momentum
to linear translational motion of a highly confined fluid can lead to significant over-estimation of the predicted
flow rates using conventional Navier-Stokes treatments. By including spin-coupling into the extended NavierStokes equations, hydrodynamic prediction is seen to be very accurate down to length scales of a few atomic
diameters4 . We also demonstrate how this knowledge, coupled with our knowledge of slip, can be used to pump
molecular fluids such as water via non-intrusive application of a rotating electric field5,6 . Finally, we show that
a complete generalisation of Navier-Stokes hydrodynamics comes about in the realisation that at the nanoscale
viscous transport is fundamentally non-local in nature. We explore this theme for homogeneous systems and
discuss the ramifications and problems yet to overcome for nanofluidic applications7,8 .
J.S. Hansen, B.D. Todd and P.J. Daivis. Phys. Rev. E 84, 016313 (2011).
S. K. Kannam, B.D. Todd, J.S. Hansen and P.J. Daivis. J. Chem. Phys. 136, 024705 (2012).
S.K. Kannam, B.D. Todd, J.S. Hansen and P.J. Daivis. J. Chem. Phys. 138, 094701 (2013).
J.S. Hansen, J.C. Dyre, P.J. Daivis, B.D. Todd and H. Bruus. Phys. Rev. E 84, 036311 (2011).
J. D. Bonthuis, D. Horinek, L. Bocquet, and R. R. Netz, Phys. Rev. Lett. 103, 144503 (2009).
S. De Luca, B.D. Todd, J.S. Hansen and P.J. Daivis. Langmuir 30, 3095-3109 (2014).
B.D. Todd, J.S. Hansen and P.J. Daivis. Phys. Rev. Lett. 100, 195901 (2008)
B.A. Dalton, P.J. Daivis, J.S. Hansen and B.D. Todd. Phys. Rev. E 88, 052143 (2013).
A New Approach For Solving A Sparse Linear System With Periodic Boundary Conditions
Minh Tran
Flinders University, Adelaide, Australia
email: [email protected]
Differential equations (DE) can be used to mathematical describe useful physical systems. These equations
often have additional constraints (boundary conditions) imposed on by the physical systems. One type of
boundary conditions is the periodic boundary conditions (PBC). Numerical solution of a DE system with PBC
involves discretizing the system, resulting in a cyclic tridiagonal system. This presentation will present a new,
efficient and robust parallel algorithm for solving such a system with time complexity of O(log(n)) on a parallel
computing platform. Furthermore, this is the first robust algorithm capable of solving a cyclic tridiagonal
system that is not diagonally dominant.
Extruding Complicated Fluid Structures
Hayden Tronnolone
University of Adelaide, Adelaide, South Australia, Australia
email: [email protected]
Coauthors: Yvonne Stokes and Darren Crowdy
The extrusion of a very viscous fluid through a die involves a range of physical processes; however, the relative
importance of each of these is not well understood. As a first step towards a better understanding, this process
is modelled as a Stokes flow driven by both surface tension and gravity. Applying a slenderness approximation
yields two coupled systems of equations applicable to dies of arbitrary connectivity that readily reveal the effects
of the physical processes under consideration. These effects are analysed and demonstrated though examples,
including the application to microstructured optical fibre fabrication.
A new mode of instability in compressible boundary-layer flows
Adam Tunney
University of Auckland, Auckland, New Zealand
email: [email protected]
In low disturbance environments such as aerodynamic flight, the initial growth of disturbances that cause
the laminar-turbulent transition process in a boundary layer can be investigated with linear stability theory
(LST). A large collection of results using LST are available in the literature, however excluded are the class of
boundary-layer flows with region of velocity overshoot. Using a compressible, heated-wall flat-plate boundary
layer with a favourable pressure gradient as a prototype, the linear stability of this class of boundary layers is
investigated numerically and analytically using LST. Along with the traditional Mack modes, a new mode of
inviscid instability is found that is localised within the region of velocity overshoot. The interaction between
the new mode and the Mack modes is investigated through viscous stability analysis.
Developing a Model of Bird Navigation
Rebecca Turner
University of Auckland, Auckland, New Zealand
email: [email protected]
Our understanding of how birds successfully navigate great distances during migration or homing still includes
many unconfirmed hypotheses. However, there are clues to the underlying mechanism of navigation in the
systematic errors birds make in their initial headings.
A simple model has been proposed to capture the initial orientation error made when a bird is attempting to
navigate home from an unfamiliar location [Postlethwaite & Walker, Journal of Theoretical Biology, (2011 &
2014)]. When comparing the predictions of the model to real experimental data one must keep in mind the
two types of assumptions present in the model. Firstly, the navigational mechanism is assumed to be a two
coordinate cognitive map system based on two environmental gradients. Secondly, the environmental gradients
considered are limited by the data available.
I will discuss the comparison of the model to real experimental data in light of the above assumptions and
suggest future directions for the development of the model.
A Cell Growth Model Adapted for Minimum Cell Size Division
Bruce van Brunt
Massey University, Palmerston North, New Zealand
email: [email protected]
Coauthors: Saima Gul and Graeme Wake
In this talk we examine a cell growth model with a division kernel that models cells dividing only after they
have reached a certain minimum size. The model features a functional differential equation of the pantograph
type. In contrast with the earlier cases, however, the determination of the steady size distribution entails an
eigenvalue that is not known explicitly, but is defined through a continuity condition. This, in turn, leads to
the study of a certain class of Dirichlet series. We show that there is a steady size distribution solution to this
A geometric approach to stationary defect solutions in one space dimension
Peter van Heijster
Queensland University of Technology, Brisbane, Queensland, Australia
email: [email protected]
Coauthors: Feng Xie and Arjen Doelman
We analyze a weakly heterogeneously perturbed system of N first order ordinary differential equations,
f (u),
t ≤ 0,
u˙ =
f (u) + εg(u), t > 0,
in a general setting. Under the assumptions that the unperturbed system is hyperbolic, possesses a heteroclinic
orbit, and that the perturbation is generic, we determine conditions such that the heterogenous system supports
a nearby defect solution. This study is motivated by previously observed defect solutions in a perturbed threecomponent FitzHugh-Nagumo equation.
Modelling Growth Variability in Cell Populations
Graeme Wake
Massey University, Auckland, New Zealand
email: [email protected]
Coauthors: Ali Zaidi and Bruce van Brunt
The study of cell population dynamics has become increasingly significant - in part because of the importance
of understanding phenomena such as tumour growth driven by epigenetic effects. These models will lead to
a better understanding of the progression of the disease. The resulting dynamical models provide a relatively
simple method for determining parameters that both regulate and enhance growth, which can help quantify the
effectiveness of cancer therapy drugs.
Populations of cells that are simultaneously undergoing growth and division are considered when the growth
is random and cells are dividing symmetrically into two or more daughter cells. Following earlier work by
Wake, van-Brunt, Kim and Cooper (Comm. Appl. Anal. 4, 2000, pp 561-574), use is made of the FokkerPlanck formulation to incorporate the stochastic effects in the growth. These models have separation of variables
solutions which suggest there is an asymptotically attracting steady-size distribution. In this work a constructive
existence theorem is obtained for the linear non-local dispersion-growth equation now with an arbitrary initial
size-distribution and with a no-flux boundary condition. This solution is unique. It is still an open question as
to whether or not the solutions obtained by separation of variables form a complete spanning set.
Inference Methods for First Few Hundred Studies
James Walker
University of Adelaide, South Australia, Australia
email: [email protected]
Coauthors: Joshua Ross and Andrew Black
Infectious diseases are a major, continuing threat to our health and well-being. Of particular concern are
pandemics, which involve a major outbreak of a novel pathogen, most commonly influenza (‘flu’). During
the early stages of such an outbreak, government authorities may undertake intensive data collection studies often termed First Few Hundred studies (FF100 studies) - in which the household members, and possibly other
contacts, of the first few hundred cases are monitored for signs of symptoms. In this talk I will discuss novel
methods appropriate for FF100 studies based upon stochastic household models of epidemics. In particular, we
will discuss the estimation of the household basic reproductive number, which determines the transmissibility
of a disease.
The flux paradox in gravitational lensing
Steve Walters
University of Tasmania, Hobart, Tasmania, Australia
email: [email protected]
An early result in the development of gravitational lensing theory is that at least one image is always magnified
due to the existence of a gravitational lens. This appears to contradict conservation of photon flux. That is,
photons should be neither created nor destroyed due to the presence of the lens. We will re-examine the origin
and nature of this paradox, and consider a new solution.
Analytical and numerical solutions of the multi-term time-space fractionaldiffusion equations with
a fractional Laplacian operator
Hao Wang
Queensland University of Technology, Brisbane, Australia
email: [email protected]
Coauthors: Fawang Liu, Ian Turner, Pinghui Zhuang and Shanzhen Chen
In this paper, we consider the one-dimensional and two-dimensional multi-term time and space fractional diffusion equations (1D-MTTSFDE, 2D-MTTSFDE). The multi-term time-fractional derivatives are defined in
the Caputo sense, whose order belongs to the interval (0,1), and the space-fractional derivative is referred to
the fractional Laplacian operator. We derive the analytical solutions of the 1D-MTTSFDE and 2D-MTTSFDE
based on the spectral representation of the fractional Laplacian operator with homogeneous boundary conditions. The nonhomogeneous boundary condition is considered as well. We propose a computationally effective
fractional predictor-corrector. It has been applied in 1D-MTTSFDE and could be extended to MTTSFDE in
higher dimensions. Finally, numerical results in both one dimensional and two dimensional are given, which are
in good agreement with the analytic solutions.
Discrete needlet approximation
Yu Guang Wang
School of Mathematics and Statistics, UNSW Australia, Sydney, NSW, Australia
Coauthors: Quoc Le Gia, Ian Sloan and Robert Womersley
Needlets are highly localised filtered radial polynomials on the sphere S d of Rd+1 , d ≥ 2, with centers at the nodes
of a suitable quadrature rule. They provide a multiscale decomposition for real L2 functions on S d . The original
needlet decomposition has its coefficients defined by an inner product integrals. In this paper, we use additional
quadrature rules, to establish a fully discrete version of the original semidiscrete needlet approximation. We
prove that the fully discrete needlet approximation is exactly equivalent to filtered hyperinterpolation, that is
to a filter-modified Fourier-Laplace series partial sum with inner products replaced by appropriate quadrature
sums. From this, we establish Lp -error bounds, 2 ≤ p ≤ ∞, for the fully discrete needlet approximation of
functions in Sobolev spaces Wps on S d for s > d/p. In particular, the Lp error for the fully discrete approximation
loses convergence order compared to the semidiscrete needlet approximation only by the exponent d/p + for
> 0 expected from the embedding of Wps (S d ) in C(S d ).
The theory is illustrated numerically for the approximation of a function of known smoothness, using symmetric
spherical designs (for both the needlet quadrature and the inner product quadrature). The power of the needlet
approximation for local approximation is shown by a numerical experiment that uses low-level needlets globally
and high-level needlets in a local region.
DES simulation for modelling patient congestion within a SA metropolitan hospital
Dale Ward
Flinders University, South Australia, Australia
email: [email protected]
Coauthors: Jerzy Filar and Shaowen Qin
The Australian public hospital system is struggling under the burden of increased demand for inpatient care.
In South Australia alone the incidents of ambulance ramping at metropolitan hospitals has increased over the
last few years and has become the focus of public attention. With the average age of the population on the rise,
this issue is only set to worsen and hospitals will need to address these issues under tighter budget restraints,
essentially doing more with less. Changes to the operating procedures of hospitals need to be made now as
patient flow congestion within hospitals can be tied to poor health outcomes.
As part of ARC linkage project, our research group is investigating the issue of patient flow congestion within
Flinders Medical Centre. In particular, the research aims at identifying early warning signs of congestion
and the experimentation of potential early interventions for avoidance or for reducing the impact. As part
of this research a discrete event based simulation model of patient flow in Flinders Medical Centre is being
developed with colleagues from the hospital. It is hoped that this simulation will assist in gaining a deeper
understanding of the underlying hospital system as well as testing possible congestion relief strategies. However,
the development of such a simulation is not straightforward due to the highly complex nature of the hospital
system. Furthermore, despite previous attempts, uptake of modelling as part of normal hospital management
practice has not been overly successful and there remains a gap between the development of models and the
buy-in from health care professionals in using them for management decision-making.
The vital role of animals in the transmission of water-borne disease in rural Australia
Edward Waters
University of Notre Dame Australia, NSW, Australia
email: [email protected]
Coauthors: Andrew Hamilton, Leesa Sidhu and Harvinder Sidhu
Though waterborne diseases such as giardia and cryptosporidium can be carried by animals commonly found in
rural locations, epidemiological studies have failed to show convincing evidence that these animals play a role
in transmission. It is possible that this is because they have not explicitly modelled the risk of transmission
from animals to humans via environmental reservoirs. Many rural Australian households rely on rainwater for
their household water supply, and this resource is easily contaminated by the droppings of animals carrying
giardia and cryptosporidium. We develop a mathematical model of the transmission of these diseases within
and between human and animal populations, with transmission between populations occurring via the drinking
of contaminated rainwater. Analysis of the model shows that endemic infection in the animal population is
sufficient to cause infection in the human population. This research has important implications for assessing
the risk of waterborne disease outbreaks in rural Australia, as current risk assessment protocols do not consider
the dynamics of disease in animal populations when estimating risk.
Long-term stochastic modelling to predict and prevent osteoarthritis
Francis Woodhouse
University of Western Australia, Perth, Australia
email: [email protected]
Coauthors: Bruce Gardiner and David Smith
Osteoarthritis afflicts around ten percent of all Australians and Americans, costing hundreds of billions of
dollars a year in treatment and lost workforce labour. Primary affecting the knees and hips, it manifests in the
slow deterioration of the articular cartilage protecting bones within diarthrodial joints. As the cartilage breaks
down, the joint becomes painful and stiff, eventually necessitating a full joint replacement if mobility is severely
compromised. Though it is partly a disease of age and genetics, it is also a disease of lifestyle and behaviour,
where obesity or otherwise abnormal joint loading can accelerate the onset of tissue degeneration. This implies
that at least some proportion of the onset risk can be mitigated with the right lifestyle changes. By integrating
what is known about the process of biomechanical damage with models of long-term cartilage homeostasis and
random daily human behaviour, we hope not only to compute per-patient likelihoods of osteoarthritis onset five
or ten years into the future, but to use this system to propose individually tailored risk reduction techniques.
Modelling the role of innate and adaptive immune responses in controlling influenza infection
Ada Yan
The University of Melbourne, Melbourne School of Population and Global Health, Parkville, Victoria, Australia
email: [email protected]
Coauthors: Pengxing Cao, Teagan Guarnaccia, Louise Carolan, Malet Aban, Robert Moss, Stephen Petrie,
Sophie Zaloumis, Jodie McVernon, Jane Heffernan, Karen Laurie and James McCaw
A study conducted by Laurie et al. has demonstrated that a primary influenza infection can protect against
subsequent challenge with related or unrelated viruses. However, this protection is exquisitely sensitive to the
time interval between exposures, and the order in which viruses are presented. We seek to understand the
mechanisms underlying temporary immunity by constructing mathematical models to describe the observed
viral dynamics.
Our model shows that the initial non-specific immune response to the first influenza virus is able to slow
down the rate of infection and death of susceptible cells, thereby preventing or delaying a second infection.
The subsequent virus-specific ‘adaptive’ immune response contributes to the resolution of infections once the
innate immune response wanes. Varying model parameters between viruses, such as the viral production rate,
transmission rate and degree of innate/adaptive immune response allows us to create a hierarchy of the ability
of infection with one influenza virus to block or delay infection with another.
However, the model includes three possible mechanisms for the innate immune response, which lead to similar
outcomes. Furthermore, by taking into account additional biological processes and/or different assumptions
about how model components interact, we can create different models which also reproduce the delay and/or
blocking of secondary infection as seen in the experimental data. Hypotheses and predictions can be constructed
from the models, which can then be experimentally tested to enable us to select the most suitable model. A
better understanding of interaction between successive infections at the within-host level will be valuable in
improving population-level models of infection, which can then be used to inform public health policy.
Rarefied gas flow generated by an oscillating sphere
Ying Wan Yap
University of Melbourne, Parkville, Victoria, Australia
email: [email protected]
Coauthors: John Sader
Flow generated by an oscillating sphere in a quiescent fluid is a classical problem, whose solution in the continuum
limit is obtained via the Navier-Stokes equations. For gas flows away from the continuum limit, the kinetic
theory of gases provides a more rigorous description. In this talk, I will discuss the effects of gas rarefaction
on the flow generated by an oscillating sphere within the framework of the Boltzmann-BGK equation. In
comparison to the continuum limit, where the flow is isothermal, non-continuum effects lead to a temperature
jump at the sphere surface and thus the flow is strongly non-isothermal.
Modelling the Motions of a Sea Ice Floe in Waves
Lucas Yiew
University of Adelaide, Adelaide, South Australia, Australia
email: [email protected]
Coauthors: Luke Bennetts and Mike Meylan
The relationship between sea ice and our global climate system is highly complex and dynamic. The distribution
and concentration of sea ice has been shown to affect large-scale oceanic and atmospheric processes. In order
to improve our understanding of the current conditions in the Arctic and Antarctic, and predict future changes
to the sea-ice cover, it is important to accurately model the physical and dynamic processes occurring in these
regions. One of these processes is the interaction between ocean waves and ice floes (discrete pieces of sea
ice). Contemporary sea ice and global oceanic circulation models do not include wave-ice interactions, and
floe-floe interactions (collisions and raftings) caused by waves. To model these processes, we start by developing
a mathematical model to predict the motions of a solitary ice floe in ocean waves, using linear potential flow
theory. The predictions of the theoretical model are validated using experimental data collected from laboratory
wave basin experiments.
Solutions to an advanced functional partial differential equation of the pantograph-type
Ali A. Zaidi1
Massey University, Auckland, New Zealand
email: [email protected]
Coauthors: Bruce van-Brunt and Graeme Wake
∂n(x, t)
∂n(x, t)
= bα2 n(αx, t) − (b + µ)n(x, t),
in {(x, t) : x, t > 0}, with an initial condition. This partial differential equation arises in cell growth models
where n(x, t) is a measure of the number density of cells of size x at time t, α > 1 (in applications it is usually 2)
is the number of daughter cells produced when a mother cell divides symmetrically, b is the frequency of division
of cells, g is the growth rate and µ is the mortality of cells. The evolution of the number density n(x, t) of cells
by size, in an unperturbed situation, is observed experimentally to asymptote to a constant shape, known as
the steady size distribution (SSD). Mathematically, this means n(x, t) ∼ T (t)y(x) as t → ∞. Previous work on
this cell growth partial differential equation deals with finding the SSD solutions. We extend the work to find
the non-SSD solutions and recover the SSD solutions for large time.
Tracking and Predicting Multiple Object Dynamics in a Complex Environment (Animal’s Behaviour)
Ayham Zaitouny
The University of Western Australia, Western Australia, Australia
email: [email protected]
Coauthors: Michael Small, Thomas Stemler and Kevin Judd
Understanding the collective motion of animals has always been a topic for biologists. Recently, mathematicians
have entered this field and explore this complex system. The collective motion refers to the movement of a group
of animals interacting among them and with surrounding environment. This interaction ensures the cohesive
form of the flock. Examples of this kind of motion are numerous and can be found in bird flocks, fish schools
and groups of deer or sheep. Understanding animal movement is a challenging mathematical exercise, that is,
this movement is driven by complex animal requirements, such as, interactions between the group individuals,
seeking for food or even interactions with different animal group. Research has been done in this field and the
specific question of understanding animal behaviour has been approached using various methods.
In this framework we report on the application of new mathematical techniques to explore and model the
collective motion of animals. Using GPS data from individual pigeons in a flock, we model the dynamics based
on forces resulting from the collective movement of the flock as well as forces that resulting from the interaction
of the individual pigeons. Our nonlinear dynamical model can explain the real observations quite well and we
point out some difficulties that arise when working with such data sets.
The numerical simulation of a fractional Black-Scholes model for European call
Hongmei Zhang
Fuzhou University, Fuzhou, China
email: [email protected]
Coauthors: Fawang Liu and Ian Turner
It is well known that the classical Black-Scholes (B-S) models puts a important role in pricing the financial
derivatives. However, the empirical data shows that the B-S model cannot correctly capture the dynamics of the
option prices such as large movement or jumps over small time step. To overcome these drawbacks other more
realistic models, which follow a jump process or a Levy process, have been proposed to model the movements
in the stock price. One of these models is FMLS (Finite Moment Log Stable) model, which can be written as
fractional partial differential equation. For the fractional differential equation, it is difficult to obtain the exact
solution or analysis solution. Therefore, in the paper, we mainly consider the numerical approximate solution
of the FMLS model in a finite domain. Unlike the existing literature (Chen (2013)), which constructed the
discrete scheme of the fractional derivative by conversing the derivative definition from the Riemann-Liouville
(R-L) fractional derivative to the Caputo fractional derivative. In this paper, directly from the R-L derivative
definition itself in the FMLS model, we construct a discrete implicit numerical scheme with the second order
accuracy. Then we analyze and prove the stability and convergence of the implict numerical scheme. Finally,
various numerical experiments suggest that the efficiency of the implicit numerical scheme. Based on the
numerical data, we also analysis the characteristics of the parameters in the FMLS model.
Speaker index
Alexander Gilbert , 23
Andrew Eberhard , 25
Azam Asanjarani , 20
Dale Ward , 23
Dion O’Neale , 24
Dwi Lestari , 22
Hongmei Zhang , 19
Jeffrey Hunter , 20
Jerzy Filar , 20
Jin Hyup Hong , 26
Kate Saunders , 25
Konstantinos Sakellariou , 24
Laleh Tafakori , 27
Lewis Mitchell , 24
Louis Bhim , 19
Mark Fackrell , 23
Maryam Alavi-Shoshtari , 25
Matthew Tam , 22
Michelle Dunbar , 21
Peter Taylor , 20
Phil Broadbridge , 26
Philipp Braun , 21
Pieter Roffelsen , 25
Pouya Baniasadi , 24
rahela abdul Rahim , 19
Robert Scheichl , 27
Soorena Ezzati , 21
Vera Roshchina , 28
yang shi , 26
Ada Yan, 20
Adam Ellery, 20
Adam Tunney, 19
Adelle Coster, 27
Adrian Grantham, 21
Adrian Noppe, 24
Aimin CHEN, 25
Alexandra Hogan, 21
Ali A. Zaidi, 17
Ali Eshragh, 20
Andras Czirok, 25
Andrea Babylon, 18
Andrew Black, 21
Andrew Cramer, 19
Andrew Holder, 22
Andrey Pototsky, 27
Anna McGann, 25
Anne Juel, 22, 30
Ashish Goyal, 20
Audrey Markowskei, 25
Awad Al-Mohy, 27
Ayham Zaitouny, 19
Barbara Johnston, 20
Billy Todd, 26
Bob Anderssen, 28
Boris Baeumer, 28
Bronwyn Hajek, 20
Bruce Gardiner, 19
Bruce van Brunt, 17
Carlo Laing, 27
Carson Drummond , 17
Catherine Penington, 18
Catheryn Gray, 25
Chen Chen, 23
Christopher Angstmann, 19
Christopher Kellett, 24
Christopher Lustri, 26
Claire Miller, 23
Cris Hasan, 24
Daniel Ladiges, 25
David Arnold, 21
David Harman, 19
David Skene, 24
Debadi Chakraborty, 28
Dougal McQueen, 22
Duncan Farrow, 23
Dylan Lusmore, 17
Eamon Conway , 23
Edward Green, 19
Edward Waters, 28
Elena Vynogradova, 27
Ellen Muir, 17
Elliot Carr, 26
Emma Greenbank, 23
Francis Woodhouse, 24
Frank de Hoog, 18
Gary Froyland, 28, 29
Graeme Hocking, 26
Graeme Wake, 17
Guiyuan Ma, 18
Hao Wang, 20
Harish Sankaranarayanan, 19
Hayden Tronnolone, 20
Heather Davidson, 23
Hugh Possingham, 17, 32
Ian Sloan, 17
James McCaw, 21
James Nichols, 20
James Osborne, 25
James Reoch, 25
James Walker, 22
Jason Cosgrove, 19
Jason Sharples, 23
Jennifer Flegg, 27
Jeong Ryeol Choi, 24
Jerome Droniou, 17
Jesse Collis, 18
Jim Denier, 17
Jin Liang, 18
John Boland, 21
John Hearne, 18
John Knight, 26
John Mitry, 25
John Murray, 20
John Shepherd, 28
Josh Chopin, 18
Joshua Ross, 26
Karen McCulloch, 25
Kerry Landman, 27, 31
Kerry-Lyn Roberts, 24
Larry Forbes, 17
Laura Karantgis, 25
Leah Edelstein-Keshet, 21, 29
Lisa Mayo, 21
Lotte Sewalt, 23
Lucas Yiew, 24
Luigi Cirocco, 22
Luke Bennetts, 25
Luke Fullard, 26
Lynne McArthur, 26
Marianito Rodrigo, 26
Mark McGuinness, 26
Mark Nelson, 23
Mary Myerscough, 23, 31
Matthew Chan, 19
Matthew Simpson, 21
Md Hamidul Islam, 24
Md. Habibur Rahman , 18
Megan Farquhar, 17
Meksianis Ndii, 18
Melanie Roberts, 28
Michael Jackson, 22
Michael Page, 17
Michael Plank, 17
Michael Small, 25, 32
Mick Roberts, 26
Mike Chen, 20
Mingmei Teo, 21
Minh Tran, 18
Rebecca Turner, 17
Robert Moss, 26
Roslyn Hickson, 27
Rowena Ball, 26
Saber Dini, 20
Sarthok Sircar, 27
Scott McCue, 22
Sergey Suslov, 18
Shanlin Qin, 25
Sheehan Olver, 27
Shev MacNamara, 20
Shinya Miyajima, 28
Shrupa Shah, 20
Silvestru Sever Dragomir, 20
Steve Taylor, 21
Steve Walters, 24
Stuart Johnston, 18
Sue Ann Chen, 21
Thomas Witeklski, 19
Thomas Witelski, 33
Timothy Moroney, 19
Tom Dyer, 24
Tony Miller, 23
Tony Roberts, 24
Vivien Challis, 27
Vivien Kirk, 24
Wang Jin, 22
William Holmes, 26
Winston Sweatman, 24
Xin-Jiang He , 18
Yan Ding, 24
Ying Wan Yap, 25
Yvonne Stokes, 20
Zoltan Neufeld, 28
Ngamta Thamwattana, 18, 33
Nicholas Read, 23
Nick Fewster-Young, 25
Nicolas Rebuli, 22
Nobutaka Nakazono, 26
Noel Barton, 26
Owen Jepps, 26
Pascal Buenzli, 19
Peter Ballard, 25
Peter Johnston, 17
Peter van Heijster, 23
Rachael Griffiths, 21
Rachelle Binny, 18
Ravindra Pethiyagoda, 24